Решить методом вариаций:

1

yctgx + y = 2

2

= xdy, y(1) = 0

3

y + 2xy = Cos(2x + 3)

4

y - , y(1) = 1

5

y =

6

(x² + y²)dx + 2xydy = 0, y(1) = 0

7

2 yx - 1 = y²

8

y + ytgx = (x + 1)y²

9

y Cosx = (3y - 1)Sinx

10

y - y = y² + x y

11

x² y+ x y = 1

12

y = lnx - x³

13

yy -(y)² = y² y

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

1

x³ y+ y = y²

2

dx + xdy = 0

3

y - , y(1) = 2

4

x y + x - y = 0

5

y (Sin²x + 1 ) = tgy Cosx, y(0) =

6

y +

7

ln²xdy = , y(e) = 

8

9

xdy + (y - x - 1)dx = 0

10

xy² y = x² + y³

11

(2yy - 3(y)² = 4y²

12

y = y + x

13

y - xlnx = Sin5x

а) однородные:

б) неоднородные:

1

y - 4y - 12у = 0

1

y + 9y + 18у = -4х - 7

2

y - 14y + 49у = 0

2

y - 24y + 144у = 3е^5х, у(2) = 0, y(2) = -1

3

y + 6y + 10у = 0

3

y - 2y + 37у = 3Cos4x - 2Sin4x

4

y + 7у = 0, у(0) = 1, y(0) = 2

4

y + 4y - 21y = 5x² + 3x - 8, y(-1) = 0,

y(-1) = -2

5

y - 12y + 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 - 2y - 48y = Cos6x, y(0) = 2, y(0) =1

7

y + 196y = 0

7

y + 10y = 2x - 3 - e^7x

8

y - 10y = 3x + 1 + Cos4x