Решить методом вариаций:

1

y = (4Sinx - x²)y

2

xdy - ydx = dx

3

y - yctgx = 2xSinx, y( ) =

4

x y + y³ = 1

5

y - = 1+ lnx, y(1) = 2

6

dy = y(3x - 4)dx

7

y + ytgx =

8

y + = tg

9

x y = y - x , y(1) = 1

10

y - 2xy = 3xy²

11

y =

12

2xy = y

13

y - xe^x = x²

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)Cos dx + xCos dy = 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 + 8y + 12у = 0

1

y - 5y - 24у = -3х + 4

2

y - 16y + 64у = 0

2

y + 11y + 28у = 3е^4х, у(2) = 0, y(2) = -1

3

y + 6y + 18у = 0

3

y - 28y + 196у = 2Sin4x - 2Cos4x

4

y + 8у = 0, у(0) = 1, y(0) = 2

4

y - 6y + 34y = x² - 3x + 5, y(-1) = 0,

y(-1) = -2

5

y - 8y - 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 + 2y - 48y = Cos5x, y(0) = 2, y(0) =1

7

y + 256y = 0

7

y + 8y = x + 1 + 7e^4x

8

y - 8y = 3x - 2 - Cos2x