Internal problem ID [3824]
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]
\[ \boxed {\left (-x^{2}+1\right ) y y^{\prime }+y^{2} x=-2 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \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 \left (x \right ) = -\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: 0.448 (sec). Leaf size: 93
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 {\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)+c_1 x^2-2 x-c_1} y(x)\to \sqrt {\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)+c_1 x^2-2 x-c_1} \end{align*}