Find the general solution of the linear d.e
xy'+2y=2x for y=6 when x=6
Ordinary Differential Equation
2014-02-28 2:58 am
回答 (1)
2014-02-28 4:55 am
✔ 最佳答案
x(dy/dx) +2y=2xdy/dx + (2/x)y = 2
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By using integrating factor:
M(x)dy/dx + 2M(x)y/x=dM(x)y/dx=2M(x)
i.e. dM(x)/dx=2M(x)/x
∫dM(x)/M(x)=∫(2/x)dx
ln[M(x)]=2ln[x]
M(x)=x^2
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d(x^2 y)/dx=2x^2
x^2 y=∫(2x^2)dx=2/3 x^3 +C
y=2x/3+C/x^2
x=6,y=6
6=2(6)/3+C/36
C=72
收錄日期: 2021-04-13 20:10:22
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