3. Решить методом вариаций:

1

x³ y+ y = y²

2

dx + xdy = 0

3

y - , y(1) = 2

4

x y + x - y = 0

5

y (Sin²x + 1 ) = tgy Cosx, y(0) =

6

y +

7

ln²xdy = , y(e) = 

8

9

xdy + (y - x - 1)dx = 0

10

xy² y = x² + y³

11

(2yy - 3(y)² = 4y²

12

y = y + x

13

y - xlnx = Sin5x

а) однородные:

б) неоднородные:

1

y + 4y - 12у = 0

1

y + 11y + 24у = -2х + 3

2

y + 14y + 64у = 0

2

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

3

y - 6y + 18у = 0

3

y + 28y + 196у = 4Sin2x - 3Cos2x

4

y - 8у = 0, у(0) = 1, y(0) = 2

4

y + 6y + 34y = 3x² + 3x - 3, y(-1) = 0,

y(-1) = -2

5

y + 12y + 20у = 0, у(0) = 3,

y(0) = 0

5

y - 8y + 16y = e^4x

6

y + 6y = 0, у(1) = 2, y(1) = 1

6

y + 14y + 48y = Sin5x, y(0) = 2, y(0) =1

7

y + 225y = 0

7

y + 9y = -x + 1 + 3e^3x

8

y - 9y = x + 2 + Sin3x

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 + 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