Решить методом вариаций:

1

dy = y²(2x – 7)dx

2

xy + y – e^x = 0

3

y = - 2 , y(0) = 0

4

ySin²x = ylny

5

y + ytgx = y⁴Cosx, y(0) =

6

dy(x² – 36) = Sin²ydx, y(12) =

7

yx² + (1 + 2x)y – x² = 0

8

(y² – 3x²)dy + 2xtdx = 0, y(1) = 2

9

(x + 1)( y + y²) = -y

10

y =

11

y⁴ – y³y = 1

12

ytgx = y + 1

13

y = lnx – x³

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

(xy² + x)dx + (y - x²y)dy = 0

2

xy + y² = 9

3

xdx - ydy = 4xdx, y(1) = 0

4

y = y + 2x

5

y + Sin = Sin

6

y - = Sin³x  y², y( ) =1

7

y = (1 + lny + lnx)

8

y = , y(1) = 0

9

dx = 2y(y² + x)dy

10

dy - xy²dx = 2xydx

11

y - x = tg²x

12

y - 2(ctgx) y = Sin³x

13

yy = (y)²

а) однородные:

б) неоднородные:

1

y - 6y + 8у = 0

1

y + 2y + у = 5e^-8x , у(2) = 0, y(2) = -1

2

y + 8y + 16у = 0

2

y - 2y - 8у = 8x - 1

3

y - 2y + 5у = 0

3

y + 6y + 8у = 4Sin5x - Cos5x

4

y + 4y = 0, у(0) = 1, y(0) = 2

4

y +2y + 17y = 2x² + 3x, y(-1) = 0, y(-1) = -2

5

y + 2y - 8у = 0, у(0) = 3, y(0) = 0

5

y - 10y + 25y = e^4x

6

y - 3y = 0, у(1) = 2, y(1) = 1

6

y + 9y + 8y = Sin3x, y(0) = 2, y(0) =1

7

y + 36y = 0

7

y + 7y = 7x + e^2x

8

y + 5y = -x - 2Sinx