Вариант № 1

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 + y - 6у = 0

1

y - y + 13у = 3х + 1

2

y + 4 y + 4у = 0

2

y - 7y + 10у = 4е^3х, у(2) = 0, y(2) = -1

3

y - y + 8у = 0

3

y - 7y + 12у = 5Sin2x - Cos2x

4

y - у = 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^-5x

6

y +5y = 0, у(1) = 2, y(1) = 1

6

y - y - 12y = Sin3x, y(0) = 2, y(0) =1

7

y + 16y = 0

7

y - 4y = 3x + 2e^4x

8

y - y = x² + Sin7x

1

(xy² + x)dx + (y - x²y)dy = 0

2

xy + y² = 9

3

xdx - ydy = 3xdx, 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 + 3y + 2у = 0

1

y + 7y - 8у = 4х + 5

2

y - 10y + 25у = 0

2

y + 9y - 10у = 3е^7х, у(2) = 0, y(2) = -1

3

y + 8y + 7у = 0

3

y - 5y + 4у = 2Sin6x + Cos6x

4

y + у = 0, у(0) = 1, y(0) = 2

4

y - 7y + 6y = 5x² + 3, y(-1) = 0, y(-1) = -2

5

y - 6y + 5у = 0, у(0) = 3, y(0) = 0

5

y - 6y + 9y = e^3x

6

y + 2y = 0, у(1) = 2, y(1) = 1

6

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

7

y + 25y = 0

7

y - 6y = 5x + Sinx

8

y - 16y = 4x + 3 + e^-x