Типовой расчет / 3
.pdfIII
Найти решение задачи Коши для системы дифференциальных уравнений методом исключения и операционным методом.
1. |
x0 |
= x − 2y |
2. |
x0 |
= x + y |
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y0 |
= x − y |
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y0 |
= 8x + 3y |
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x(0) = 1, y(0) = 0 |
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x(0) = 0, y(0) = 2 |
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3. |
x0 |
= x − 4y |
4. |
x0 |
= x + y |
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y0 |
= x + y |
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y0 |
= −x − y |
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x(0) = 0, y(0) = 1 |
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x(0) = −2, y(0) = 1 |
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5. |
x0 |
= 2x y |
6. |
x0 |
= −x + y |
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y0 |
= x +−4y |
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y0 |
= −2x + y |
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x(0) = 1, y(0) = 0 |
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x(0) = 0, y(0) = 1 |
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x0 |
= 3x + y |
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x0 |
= 3x + y |
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7. |
y0 |
= −x + y |
8. y0 |
= −x + 5y |
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x(0) = 3, y(0) = 0 |
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x(0) = 0, y(0) = 2 |
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x0 |
= 5x y |
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x0 |
= 12x 5y |
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9. |
y0 |
= |
x +−3y |
10. y0 |
= |
5x +−12y |
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x(0) = 1, y(0) = 0 |
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x(0) = 1, y(0) = 1 |
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11. |
x0 |
= |
x − y |
12. x0 |
= −x − 10y |
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y0 |
= 4x − 3y |
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y0 |
= 2x + 3y |
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x(0) = 3, y(0) = 0 |
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x(0) = 7, y(0) = −1 |
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x0 |
= 3x y |
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x0 |
= 2x |
5y |
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13. |
y0 |
= |
x +−5y |
14. y0 |
= |
− x− |
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x(0) = 2, y(0) = 1 |
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x(0) = 7, y(0) = −1 |
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15. |
x0 |
= x − 2y |
16. x0 |
= |
x + y |
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y0 |
= 2x − 3y |
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y0 |
= −4x + y |
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x(0) = 0, y(0) = 1 |
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x(0) = 1, y(0) = 2 |
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x0 |
= 3x + 4y |
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x0 |
= 4x + 15y |
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17. |
y0 |
= |
−−x + y |
18. y0 |
= −3x − 2y |
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x(0) = 0, y(0) = 3 |
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x(0) = 7, y(0) = −1 |
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19. |
x0 |
= −3x + 2y |
20. x0 |
= 3x − y |
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y0 |
= −2x + y |
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y0 |
= x + y |
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x(0) = 1, y(0) = 0 |
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x(0) = 1, y(0) = 2 |
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x0 |
= 12x + 5y |
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x0 |
= 5x + 4y |
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21. |
y0 |
= −5x + 12y |
22. y0 |
= −x + y |
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1
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x(0) = 2, y(0) = 2 |
x(0) = 3, y(0) = −4 |
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x0 |
= 5x + 15y |
x0 |
= 3x + y |
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23. |
y0 |
= −3x − y |
24. y0 |
= −4x − y |
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x(0) = 1, y(0) = 1 |
x(0) = 7, y(0) = −1 |
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25. |
x0 |
= |
x |
26. x0 |
= x − 2y |
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y0 |
= −5x − 2y |
y0 |
= 2x + 5y |
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x(0) = −1, y(0) = 7 |
x(0) = 2, y(0) = −2 |
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27. |
x0 |
= 3x + 2y |
28. x0 |
= −x − y |
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y0 |
= −10x − y |
y0 |
= x − y |
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x(0) = −1, y(0) = 7 |
x(0) = 1, y(0) = 0 |
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29. |
x0 |
= −x + y |
30. x0 |
= −8y |
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y0 |
= −y |
y0 |
= 2x |
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x(0) = 2, y(0) = 1 |
x(0) = 2, y(0) = 0 |
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IV
Найти общее решение системы матричным способом.
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x0 = −3x − y − z |
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1.y0 = 6x + 6y + 5z
z0 = −x − 3y − 2z
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x0 |
= |
2x |
y |
− |
z |
3. |
y0 |
= |
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− y |
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z0 |
= |
2y−+ z |
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x0 |
= −x + 2y + 3z |
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5.y0 = 2x − 3y − 2z
z0 = −x + 3y + 3z
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x0 = 2x + y + z |
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7.y0 = −y − 2z
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z0 |
= |
y − 4z |
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x0 |
= |
x − 2y − 2z |
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9.y0 = x + 4y + 2z
z0 = −x − y + z
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x0 = 3x − y − z |
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11.y0 = −x + 5y + z
z0 = −2x + y + 2z
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x0 = x + 3y |
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2.y0 = 3x − 2y − z
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z0 |
= |
−y + z |
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x0 |
= |
3x − 2y + 2z |
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4.y0 = 4x − 3y − 2z
z0 = x − y + 2z
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x0 = 2x − y |
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6.y0 = 4x − 3y − 2z
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z0 |
= |
−z |
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x0 |
= |
3x + y + z |
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8.y0 = 2x + 2y + z
z0 = x + y + 3z
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x0 = 5x + 2y + 2z |
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10.y0 = 3x + 4y − 3z
z0 = −2x − 2y + 3z
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x0 = x + y + z |
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12.y0 = 3x + y + z
z0 = 3x − 2y + 4z
2
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x0 = 2x + 2y |
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13.y0 = 2x − 2y − z
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z0 |
= |
−y + 2z |
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x0 |
= |
−x + y + z |
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15.y0 = x − y + z
z0 = x + y + z
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x0 = 6x + 5y + 6z |
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17.y0 = −3x − 2y − z
z0 = −x − y − 3z
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x0 = 2y − z |
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19.y0 = x + y − z
z0 = −x + y + z
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x0 = |
x − y |
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21.y0 = −x − 2y + 3z
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z0 |
= |
3y + z |
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x0 |
= |
−3x − 2y + 2z |
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23.y0 = 3x + 3y − z
z0 = 2x + 3y − z
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x0 = x + y + z |
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25.y0 = x − y + z
z0 = x + y − z
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x0 = 4x + 3y − 2z |
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27.y0 = x + y + z
z0 = x + 3y + z
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x0 |
= |
x + 2y + z |
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29. |
y0 |
= |
− |
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x + z |
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z0 |
= |
4x |
− |
4y + 2z |
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x0 = x − y + z |
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14.y0 = 2x − 2y + z
z0 = −5x + 2y + 4z
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x0 = x − y + z |
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16.y0 = x + y − z
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z0 |
= |
2x − y |
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x0 |
= |
3x − y + 3z |
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18.y0 = 3x − y + 2z
z0 = −2x + 2y − 3z
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x0 = 3x − 6y |
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20.y0 = −6x − 3y + 2z
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z0 |
= |
2y + 3z |
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x0 |
= |
2x + y − z |
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22.y0 = 2x + 3y − 2z
z0 = −2x + 4y − 3z
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x0 = −3x − 2y + 4z |
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24.y0 = −x + 2y + z
z0 = −2x + 2y + 3z
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x0 = 4x − 5y + 2z |
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26.y0 = x + y − z
z0 = x + 2y − 2z
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x0 |
= |
− |
2x + 3y |
2z |
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28. |
y0 |
= |
y |
2z− |
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z0 |
= |
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−z |
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− |
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x0 |
= |
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−y − z |
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30.y0 = x + 2y − z
z0 = −2x − 2y + z
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