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求微分方程(1+y²)xdx+(1+x²)ydy=0通解
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两边除以(1+x²)(1+y²),移项ydy/(1+y²)=-xdx/(1+x²)1/2*d(1+y²)/(1+y²)=1/2*d(1+x²)/(1+x²)ln(1+y²)=ln(1+x²)+Cy²+1=C(x²+1)就是所求方程的通解
咨询记录 · 回答于2022-09-24
求微分方程(1+y²)xdx+(1+x²)ydy=0通解
不对呀
两边除以(1+x²)(1+y²),移项ydy/(1+y²)=-xdx/(1+x²)1/2*d(1+y²)/(1+y²)=1/2*d(1+x²)/(1+x²)ln(1+y²)=ln(1+x²)+Cy²+1=C(x²+1)就是所求方程的通解