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 Sin³xCos²x = y² + 1

2

2xydx - (x² + y²) dy = 0, y(1) = 1

3

y + 2xy =

4

y +

5

y + xy² = 0, y(1) = 0

6

yCosx + ySinx = 1

7

y = - 7, y(0) = 0

8

(x - y)dx + xdy = 0

9

y - x y = 4(1 + x² y)

10

x² y + y² - 2xy = 0

11

y = x³ + Sinx

12

2yy - 3(y )² = 4y²

13

2x y y = (y)² + 1

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