Internal problem ID [3937]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 691.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{3} y^{\prime }-\left (-x^{2}+1\right ) \left (1+y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 29
dsolve(x*y(x)^3*diff(y(x),x) = (-x^2+1)*(1+y(x)^2),y(x), singsol=all)
\[ \frac {x^{2}}{2}-\ln \left (x \right )+\frac {y \left (x \right )^{2}}{2}-\frac {\ln \left (1+y \left (x \right )^{2}\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.095 (sec). Leaf size: 61
DSolve[x y[x]^3 y'[x]==(1-x^2)(1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1-W\left (-\frac {e^{x^2-1-2 c_1}}{x^2}\right )} y(x)\to \sqrt {-1-W\left (-\frac {e^{x^2-1-2 c_1}}{x^2}\right )} \end{align*}