Internal problem ID [3316]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 574.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y y^{\prime }+2 x^{2}+x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 91
dsolve((-x^2+1)*y(x)*diff(y(x),x)+2*x^2+x*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {\ln \left (x -1\right ) x^{2}-\ln \left (x +1\right ) x^{2}+c_{1} x^{2}-\ln \left (x -1\right )+\ln \left (x +1\right )-c_{1}-2 x} \\ y \relax (x ) = -\sqrt {\ln \left (x -1\right ) x^{2}-\ln \left (x +1\right ) x^{2}+c_{1} x^{2}-\ln \left (x -1\right )+\ln \left (x +1\right )-c_{1}-2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.475 (sec). Leaf size: 61
DSolve[(1-x^2)y[x] y'[x]+2 x^2+x y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-2 \left (\left (x^2-1\right ) \tanh ^{-1}(x)+x\right )+c_1 \left (x^2-1\right )} \\ y(x)\to \sqrt {-2 \left (\left (x^2-1\right ) \tanh ^{-1}(x)+x\right )+c_1 \left (x^2-1\right )} \\ \end{align*}