Решить методом вариаций:

1

y =(49 - х²)у

2

y = , у(1) = 1

3

y =

4

y + ytgx = y⁴tgx, x(0) = 1

5

y =

6

yx² = y² - 2x²

7

x³y + y = y²

8

y + y = , y(0) =

9

yy =

10

(1 - x²)dy-xydx = 2xydx = 2xy²dx

11

y - xlnx = 0

12

y + (y)² = 0

13

y x - lnx = y

а) однородные:

б) неоднородные:

1

y + 2y - 8у = 0

1

y - 6y + 13у = -4х + 8

2

y - 2 y + у = 0

2

y - 10y + 25у = -3е^-7х, у(2) = 0, y(2) = -1

3

y + 6y + 13у = 0

3

y - 7y - 8у = -2Sin3x + 4Cos3x

4

y + 9у = 0, у(0) = 1, y(0) = 2

4

y - 8y + 25y = 7x² - 4x, y(-1) = 0, y(-1) = -2

5

y - 8y + 7у = 0, у(0) = 3, y(0) = 0

5

y + 12y + 36y = e^-6x

6

y - 5y = 0, у(1) = 2, y(1) = 1

6

y + 2y + 2y = Cos7x, y(0) = 2, y(0) =1

7

y - 64y = 0

7

y + 6y = 4x + e^8x

8

y + 8y = -x + Cos4x

1

y = 2^x+y

2

xy + y + , y(e) = e

3

y + 2xy = (3x + 4)

4

y =

5

y tgx - y = 2, y( ) = 1

6

y - =

7

,y(0) = 0

8

y =

9

dy -

10

x -

11

y =

12

yy = ( y )²

13

xy = yln

а) однородные:

б) неоднородные:

1

y + 6y + 8у = 0

1

y + 8y + 25у = 7х + 5

2

y - 8y + 4у = 0

2

y - 9y + 8у = 4е^2х, у(2) = 0, y(2) = -1

3

y - 6y + 13у = 0

3

y + 9y + 8у = Sin4x - 2Cos4x

4

y - 16y = 0, у(0) = 1, y(0) = 2

4

y + 8y + 17y = 3x² + 2x-10,

y(-1) = 0, y(-1) = -2

5

y + 6y - 7у = 0, у(0) = 3, y(0) = 0

5

y - 12y + 36y = 3e^3x

6

y - 2y = 0, у(1) = 2, y(1) = 1

6

y + y + y = Cos4x, y(0) = 2, y(0) =1

7

y + 81y = 0

7

y + 10y + 9y = Sin8x

8

y - 16y = 4x + 3 + e^-x