Решить методом вариаций:

1

ytgx - y = 6

2

y = , y(1) = 0

3

y -

4

xy + y = y³, y(1) = 1

5

xdy + (y - e^x)dx = 0

6

(xy - y)arctg = x

7

xdy + ylnxdx = ylnydx, y(1) = 1

8

SinyCosxdy = CosySinxdx

9

y + ytgx = y²tg²x

10

y -

11

y = - x²

12

y + y = -x²(y)²

13

2 y = 3 y

а) однородные:

б) неоднородные:

1

y - 9y + 8у = 0

1

y - 6y + 13у = 5x + 4

2

y - 10y + 25у = 0

2

y - 9y +8у = 8e^3x , у(2) = 0, y(2) = -1

3

y + 8y + 25у = 0

3

y - 7y - 8у = 4Cos2x - Sin2x

4

y + 16y = 0, у(0) = 1, y(0) = 2

4

y +2y + 5y = 3x² + x - 8,

y(-1) = 0, y(-1) = -2

5

y - 10y + 9у = 0, у(0) = 3, y(0) = 0

5

y - 2y + y = -7e^x

6

y - 6y = 0, у(1) = 2, y(1) = 1

6

y + 8y + 16y = Cos8x, y(0) = 2,

y(0) =1

7

y + 100y = 0

7

y - 3y = 4x + Sin3x

8

y - 4y = -x + e^2x

1

yy =

2

xdy - ydx = , y(1) = 0

3

y+2xy =

4

y - xy = 2(1 + x² y), y(1) = 3

5

y + ytg = Sinx

6

(x + y)dx + xdy = 0

7

y = 2y + 1

8

y + , y(2) = 1

9

dx = (2y -2xy)dy

10

xy + 2y + x⁵y³e^x = 0

11

y - xSinx = 0

12

y y + (y)² = 1

13

x³ y + x² y = 1

а) однородные:

б) неоднородные:

1

y + 8y + 25у = 0

1

y + 8y + 17у = 5х + 8

2

y + 9y + 8у = 0

2

y + 6y + 8у = 5е^9х, у(2) = 0, y(2) = -1

3

y + 10y + 25у = 0

3

y - 4y + 3у = 7Sin4x + 5Cos4x

4

y - 16у = 0, у(0) = 1, y(0) = 2

4

y + 3y + 2y = 7x² +4x - 3, y(-1) = 0, y(-1) = -2

5

y - 8y - 9у = 0, у(0) = 3, y(0) = 0

5

y - 4y + 4y = 3e^2x

6

y - 7y = 0, у(1) = 2, y(1) = 1

6

y + 2y + 2y = Sin3x, y(0) = 2, y(0) =1

7

y + 144y = 0

7

y - 8y = 7x + e^-x

8

y + 5y = 3x + 1 - Sin5x