3. Решить методом вариаций:

1

y = (1 - x²)y

2

y =

3

x + 2xy =

4

y = + 3tg , y(0) = 0

5

xdy - ydx =

6

x²y + y² = 4, y(2) = 3

7

y - = lnx, y(1) = 2

8

xyy = 1 = x²

9

y + ytgx = y⁴Sin³x

10

2xdy = (y + 3x²)dx

11

yy - yy lny = ln(y)²

12

(1 + x²) y - 2x y = 0

13

- xe^x - x = 0

а) однородные:

б) неоднородные:

1

y + y - 6у = 0

1

y - y + 13у = 3х + 1

2

y + 4 y + 4у = 0

2

y - 7y + 10у = 4е^3х, у(2) = 0, y(2) = -1

3

y - y + 8у = 0

3

y - 7y + 12у = 5Sin2x - Cos2x

4

y - у = 0, у(0) = 1, y(0) = 2

4

y +2y + 17y = 2x² + 3x, y(-1) = 0, y(-1) = -2

5

y - 2y - 8у = 0, у(0) = 3, y(0) = 0

5

y + 10y + 25y = e^-5x

6

y +5y = 0, у(1) = 2, y(1) = 1

6

y - y - 12y = Sin3x, y(0) = 2, y(0) =1

7

y + 16y = 0

7

y - 4y = 3x + 2e^4x

8

y - y = x² + Sin7x

1

y =(49 - х²)у

2

y = , у(1) = 1

3

y -

4

y + ytgx = y⁴tgx, x(0) = 1

5

y =

6

yx² = y² - 2x²

7

x³y + y = y²

8

y + y = , y(0) =

9

yy =

10

(1 - x²)dy-xydx = 2xydx

11

y - xlnx = 0

12

y + (y)² = 0

13

y x - lnx = 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