微分方程的通解(xy^2+x)dx+(y-x^2y)dy=0.书上答案是(1+y^2)/(1-x^2)=C
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微分方程的通解(xy^2+x)dx+(y-x^2y)dy=0.书上答案是(1+y^2)/(1-x^2)=C
微分方程的通解(xy^2+x)dx+(y-x^2y)dy=0.书上答案是(1+y^2)/(1-x^2)=C
微分方程的通解(xy^2+x)dx+(y-x^2y)dy=0.书上答案是(1+y^2)/(1-x^2)=C
(xy^2+x)dx+(y-x^2y)dy=0
x(y^2+1)dx=y(x^2-1)dy
y/(y^2+1)dy=x/(x^2-1)dx
2y/(y^2+1)dy=2x/(x^2-1)dx
两边积分,得
ln(y^2+1)=ln(x^2-1)+lnc
y²+1=c【x²-1】
即
(1+y^2)/(1-x^2)=C