Internal problem ID [3690]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 965.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {x y \left (y^{\prime }\right )^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x=0} \end {gather*}
✗ Solution by Maple
dsolve(x*y(x)*diff(y(x),x)^2+(a+x^2-y(x)^2)*diff(y(x),x)-x*y(x) = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.366 (sec). Leaf size: 112
DSolve[x y[x] (y'[x])^2+(a+x^2-y[x]^2)y'[x]-x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {c_1 \left (x^2+\frac {a}{1+c_1}\right )} \\ y(x)\to -\sqrt {\left (\sqrt {a}-i x\right )^2} \\ y(x)\to \sqrt {\left (\sqrt {a}-i x\right )^2} \\ y(x)\to -\sqrt {\left (\sqrt {a}+i x\right )^2} \\ y(x)\to \sqrt {\left (\sqrt {a}+i x\right )^2} \\ \end{align*}