求(y^2-6x)dy/dx+2y=0的通解
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求(y^2-6x)dy/dx+2y=0的通解
求(y^2-6x)dy/dx+2y=0的通解
求(y^2-6x)dy/dx+2y=0的通解
:∵(y²-6x)dy/dx+2y=0 ==>dy/y²-6xdy/y^4+2dx/y³=0 (等式两端同除y^4)
==>dy/y²+2xd(1/y³)+d(2x)/y³=0
==>d(1/y)=d(2x/y³)
==>1/y=2x/y³+C (C是积分常数)
==>y²=2x+Cy³
∴原方程的通解是y²=2x+Cy³.