Решить методом вариаций:

1

y = (27 + x³) y²

2

y =

3

y - = x³ + 4, y(1) = 2

4

xyy = 1- x²

5

y Cosx - ySinx = 2x, y(0) = 1

6

(x + 2y)dx - xdy = 0

7

xy = y(1 + lny - lnx), y(1) = e

8

ySinx = ylny

9

y - = (x + 1)³

10

y +

11

y = y + x²

12

yy = (y )²

13

y - 2ctgx y = Sin³x

а) однородные:

б) неоднородные:

1

y - 8y + 15у = 0

1

y + 11y + 24у = -6х - 1

2

y - 18y + 81у = 0

2

y - 3y - 28у = 6е^7х, у(2) = 0, y(2) = -1

3

y - 4y + 18у = 0

3

y - 26y + 169у = 3Cos5x - 2Sin5x

4

y - 9у = 0, у(0) = 1, y(0) = 2

4

y + 4y + 29y = -2x² + 3x + 7, y(-1) = 0,

y(-1) = -2

5

y - 7y + 12у = 0, у(0) = 3, y(0) = 0

5

y - 6y + 9y = e^3x

6

y + 7y = 0, у(1) = 2, y(1) = 1

6

y - 15y + 56y = Sin4x, y(0) = 2, y(0) =1

7

y + y = 0

7

y + 7y = 6x + 5e^5x

8

y - 7y = -2x - 1 + 3Sin4x

1

y tgx - 3y = 1

2

y =

3

y - ytgx = , y(0) = 1

4

(x - y)ydx - x²dy = 0

5

y² + x² y = xy y, y(1) = 1

6

7

y - - 1 - x = 0

8

yCosx = ylny, y(0) = e

9

(1 - x²) y + xy = 2

10

(x + y⁵)dy = ydx

11

(1 + x²) y - 2x y = 0

12

y - xe^x - x² = 0

13

yy - yy lny = (y)²

а) однородные:

б) неоднородные:

1

y + 8y + 15у = 0

1

y - 11y + 30у = -6х - 1

2

y - 20y + 100у = 0

2

y - 32y - 256у = 3е^4х, у(2) = 0, y(2) = -1

3

y - 6y + 25у = 0

3

y - 8y + 52у = 8Cos4x - 3Sin4x

4

y - 10у = 0, у(0) = 1, y(0) = 2

4

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

y(-1) = -2

5

y+ 7y + 12у = 0, у(0) = 3, y(0) = 0

5

y - 4y + 4y = e^2x

6

y + 8y = 0, у(1) = 0, y(1) = 1

6

y + 15y + 56y = Sin3x, y(0) = 2, y(0) =1

7

y + 9y = 0

7

y + 5y = 6x + 5e^8x

8

y - 5y = 5x + 4 - 7Cos7x