Дифференциальные уравнения.

4.1 xy^|+1 = e^y

4.2

4.3 (1+x²) y^||-2xy^| = 0

4.4 xy^|+1 = e^y

4.5

47.6

4.7

4.8

4.9.

4.10

4.11 y^|-xy² = 2xy

4.12 xy^|+y = y², y(1)=0, 5

4.13

4.14 z^| = 10^x+z

4.15

4.16

4.17 2x²yy^|+y² = 2

4.18 y^| ctgx+y = 2, y(0)=-1

4.19 y^| sinx = y lny, y(p/2)=1

4.20 x²y^| - cos2y = 1

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9 ydx – (x+y)dy = 0

5.10(y²-3x²)dx – 2xydy = 0

5.11 (x²+2xy-y²)dx+(y²+2xy-x²)dy = 0

5.12

5.13 (y²-2xy)dx+x²dy = 0

5.14 y²+x²y^| = xyy^|

5.15(x²+y²)y^| = 2xy

5.16 xy^|-y=x

5.17

5.18

5.19

5.20

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6.1 xy^|+y = y² ln x

6.2 (2x+1) y^| = 4x+2y

6.3 x² dy = (2xy+x²-y)dx

6.4 2x (x²+y) dx = dy

6.5 xy^|+(x+1)y = 3x²e^-x

6.6 (x+y²)dy = ydx

6.7 (sin²y+x ctgy) y^| = 1

6.8 (2x+y) dy = ydx+4 lny dy

6.9 xy dy = (y²+x) dx

6.10y^| x³ siny = xy^|-2y

6.11(xy+e^x) dx-x dy = 0

6.12y = x (y^|-x cosx)

6.13(xy^|-1) lnx = 2y

6.142e^y-xy^| = 1

6.15xy²y^| = x²+y³

6.16xy^|-2x² = 4y

6.172y^|- =

6.18(2x²y lny-x) y^| = y

6.192xy^|-6y = -x²

6.20y^|+y cosx = sinx cosx

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7.1 2xy^| y^|| = y^|2-1

7.2 y^|2+2yy^|| = 0

7.3 yy^||+1=y^|2

7.4 y = 2(y^||-1) ctgx

7.5 yy^|| = y^|2-y^|3

7.6 2yy^|| = y²+y^|2

7.7 y^||2+y^| = xy^||

7.8 y^||+y^|2=2e^-y

7.9 y^||2 = y^|2+1

7.102y^| (y^||+2) = xy^||2

7.11y^|2 = (3y-2y^|) y^||

7.12y^|| (2y^|+x) = 1

7.13(1-x²) y^||+xy^| = 2

7.14yy^||-2yy^| lny = y^|2

7.15(y^|+2y) y^|| = y^|2

7.16xy^|| = y^|+x

7.17yy^||+y = y^|2

7.182yy^|3+y^|| = 0

7.19y^|| (3y+4) – 3y^|2 = 0

7.202xy^|y^|| = y^|2+1

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8.1 a) y^||+y^|-2y = 0

b) y^||+3y^|-4y = e^-4x+xe^-x

8.2 a) y^||-2y = 0

b) y^||+2y^|-3y = x²e^x

8.3 a) y^||-4y^|+5y = 0

b) y^||-4y^|+8y = e^2x+sin2x

8.4 a) y^||+4y = 0

b) y^||-2y^|+y = 6xe^x

8.5 a) 4y^||+4y^|+y = 0

b) y^||-y = 4shx

8.6 a) y-3y^||+3y^|-y = 0

b) y^||+4y^|+3y=chx

8.7 a) y-3y^|+2y = 0

b) y^||+2y^|+2y = xe^-x

8.8 a) y^||+4y^|+3y = 0

b) y^||+y^| = 2cosx+e^x

8.9 a) 2y^||-5y^|+2y = 0

b) y^||+y = 4sinx

8.10a) y^||+2y^|+10y = 0

b) y^||-3y^|+2y = x cosx

8.11. a) y^||-2y^|+y = 0

b) y^||+y = 4xe^x

8.12. a) y-6y^||+9y^| = 0

b) y^||+y^|-2y = 3xe^x

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8.13a) y^||+2y^|+y = 0

b) y^||-3y^|+9y = x cosx

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37.13.

8.14a) y-y^||-y^|+y = 0

b) y^||-2y^|-3y = e^4x

8.15a) y+8y^||+16y^| = 0

b) y^||-y = 2e^x-x²

8.16a) y^||+4y^|+3y = 0

b) y^||-3y^|+2y = sinx

8.17a) y^||+y^|-2y = 0

b) y^||-5y^| = 3x²+sin5x

8.18a) y^||-3y^|+2y = 0

b) y^||+y = x sinx

8.19a) y^||-5y^|+4y = 0

b) y^||-9y = e^3x cosx

8.20a) y^||+2y^|-3y = 0

b) y^||+4y^|+4y = xe^2x

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