3. Решить методом вариаций:

1

y = (4Sinx - x²)y

2

dxy - 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 + 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

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 + 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