using the substitution y=ux,find the general solution of (x^

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using the substitution y=ux,find the general solution of (x^2)y*dy/dx=x^3+(x^2)y-y^3
用y=ux解微分方程

(x^2)y dy/dx=x^3+(x^2y)-y^3
y=ux dy=udx+xdu
(x^2)ux*(udx+xdu)=(x^3+x^3u-x^3u^3)dx
x^4udu=x^3(1+u-u^2-u^3)dx
udu/(1+u-u^2-u^3)=dx/x
general solution
(1/4)ln[|1+u|/|1-u|] +(1/2)*(1/(1+u))+C=ln|x|

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