Решить методом вариаций:

1

y = x(y³ + 8)

2

y =

3

y = 2xy + x³

4

y =

5

Sin²xdy = 3y²dx, y( ) = 1

6

y - y = 2

7

x y + y = y²

8

y+ ytgx = Sinx y², y(0) = 1

9

dx + xdy = 0

10

xdy = (y + x²)dx

11

y - x = 4y²x

12

yy = (y)²

13

y - 2ctgx y = Sinx

а) однородные:

б) неоднородные:

1

y + 2y - 15у = 0

1

y - y - 30у = -6х - 1

2

y + 20y + 100у = 0

2

y - 30y - 225у = 5е^2х, у(2) = 0, y(2) = -1

3

y + 6y + 25у = 0

3

y + 8y + 52у = - Sin5x + 2Cos5x

4

y + 10у = 0, у(0) = 1, y(0) = 2

4

y + 12y + 35y = 7x² + 2x + 4, y(-1) = 0,

y(-1) = -2

5

y+ y - 12у = 0, у(0) = 3, y(0) = 0

5

y + 4y + 4y = e^-2x

6

y - 8y = 0, у(1) = 2, y(1) = 1

6

y + y - 56y = Cos3x, y(0) = 2, y(0) =1

7

y + 16y = 0

7

y + 4y = 5x + 4e^6x

8

y - 4y = 4x + 3 + 6Cos5x

1

dy = y²(2x – 7)dx

2

xy + y – e^x = 0

3

y = - 2 , y(0) = 0

4

ySin²x = ylny

5

y + ytgx = y⁴Cosx, y(0) =

6

dy(x² – 36) = Sin²ydx, y(12) =

7

yx² + (1 + 2x)y – x² = 0

8

(y² – 3x²)dy + 2xydx = 0, y(1) = 2

9

(x + 1)( y + y²) = -y

10

y =

11

y⁴ – y³y = 1

12

ytgx = y + 1

13

y = lnx – x³

а) однородные:

б) неоднородные:

1

y + 3y + 2у = 0

1

y + 7y - 8у = 4х + 5

2

y - 10y + 25у = 0

2

y + 9y - 10у = 3е^7х, у(2) = 0, y(2) = -1

3

y + 8y + 7у = 0

3

y - 5y + 4у = 2Sin6x + Cos6x

4

y + у = 0, у(0) = 1, y(0) = 2

4

y - 7y + 6y = 5x² + 3, y(-1) = 0, y(-1) = -2

5

y - 6y + 5у = 0, у(0) = 3, y(0) = 0

5

y - 6y + 9y = e^3x

6

y + 2y = 0, у(1) = 2, y(1) = 1

6

y + y + y = Cos4x, y(0) = 2, y(0) =1

7

y + 25y = 0

7

y - 6y = 5x + Sinx

8

y - 16y = 4x + 3 + e^-x