用MATLAB求解微分方程dy/dx-2y/(x+1)=(x+1)^5/2
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用MATLAB求解微分方程dy/dx-2y/(x+1)=(x+1)^5/2
用MATLAB求解微分方程dy/dx-2y/(x+1)=(x+1)^5/2
用MATLAB求解微分方程dy/dx-2y/(x+1)=(x+1)^5/2
dsolve('Dy-2*y/(x+1)=(x+1)^5/2')
ans =
(C2*exp((2*t)/(x + 1)))/4 - (3*x)/2 - (15*x^2)/4 - 5*x^3 - (15*x^4)/4 - (3*x^5)/2 - x^6/4 - 1/4
对应的齐次方程为
dy/dx-2y/(x+1)=0
dy/y=2dx/(x+1)
ln|y|=2ln|x+1|+ln|C1|
y=C1(x+1)²
用常数变易法,把C1换成u,即令
y=u(x+1)² ...
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对应的齐次方程为
dy/dx-2y/(x+1)=0
dy/y=2dx/(x+1)
ln|y|=2ln|x+1|+ln|C1|
y=C1(x+1)²
用常数变易法,把C1换成u,即令
y=u(x+1)² ①
那么 dy/dx=u '(x+1)²+2u(x+1)
代入所给非齐次方程,得
u '=(x+1)^(1/2)
两端积分,得 u=2/3 (x+1)^(3/2) +C
把上式代入①式,即得所求方程的通解为y=(x+1)²[2/3 (x+1)^(3/2)+C]
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