Решить методом вариаций:

1

e^-y(1 + y) = 1

2

xln dy - ydx = 0

3

y + 2xy = ctg3x

4

xdy + ydx =3 ydy, y(0) = 1

5

xy + y = 1, y(1) = 1

6

xy + y = lnx

7

y - xy = 2(1 + x²y), y(1) = 2

8

y + ytgx = y⁴  tg²x

9

Sinxdy =

10

3y² y + y³ - x - 1 = 0

11

y + x =

12

y + y =

13

+ = 1

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

1

y = (1 - x²)y

2

y =

3

x + 2xy =

4

y = + 3tg , y(0) = 0

5

xdy - ydx =

6

x²y + y² = 4, y(2) = 3

7

y - = lnx, y(1) = 2

8

xyy = 1 = x²

9

y + ytgx = y⁴Sin³x

10

2xdy = (y + 3x²)dx

11

yy - yy lny = ln(y)²

12

(1 + x²) y - 2x y = 0

13

y - xe^x - x = 0

а) однородные:

б) неоднородные:

1

y - 2y - 8у = 0

1

y - 6y + 13у = 4х + 1

2

y - 8y + 16у = 0

2

y - 3y + 2у = 4е^-5х, у(2) = 0, y(2) = -1

3

y + 4y + 8у = 0

3

y + 6y + 9у = 7Sin2x + 8Cos2x

4

y - 9у = 0, у(0) = 1, y(0) = 2

4

y + 3y + 2y = 5x² + x + 1, y(-1) = 0, y(-1) = -2

5

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

5

y - y - 6y = e^3x

6

y + 6y = 0, у(1) = 2, y(1) = 1

6

y - 2y + 5y = Cos5x, y(0) = 2, y(0) =1

7

y + 49y = 0

7

y - 6y = 3x + e^2x

8

y - 8y = x + Sin7x