3. 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

11

y - xlnx = 0

12

y + (y)² = 0

13

y x - lnx = y

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

1

yy =

2

xdy - ydx = , y(1) = 0

3

y+2xy =

4

y - xy = 2(1 + x² y), y(1) = 3

5

y + ytg = Sinx

6

(x + y)dx + xdy = 0

7

y = 2y + 1

8

y + , y(2) = 1

9

dx = (2y -2xy)dy

10

xy + 2y + x⁵y³e^x = 0

11

y - xSinx = 0

12

y y + (y)² = 1

13

x³ y + x² y = 1

а) однородные:

б) неоднородные:

1

y - 8y + 12у = 0

1

y + 3y - 18у = -5x + 8

2

y + 14y + 49у = 0

2

y + 24y +144у = 12e^7x , у(2) = 0,

y(2) = -1

3

y - 6y + 10у = 0

3

y + 2y + 37у = 4Cos8x - 7Sin8x

4

y - 7y = 0, у(0) = 1, y(0) = 2

4

y +10y + 21y = -5x² +2x + 1,

y(-1) = 0, y(-1) = -2

5

y + 8y - 20у = 0, у(0) = 3, y(0) = 0

5

y - 10y + 25y = e^5x

6

y + 5y = 0, у(1) = 2, y(1) = 1

6

y - 14y + 48y = Sin6x, y(0) = 2,

y(0) =1

7

y + 169y = 0

7

y + 11y = x + e^8x

8

y - 11y = 2x - 3+ Sin3x