Internal problem ID [3603]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 875.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)^2+(1-x^2*y(x))*diff(y(x),x)-x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\ln \left (x \right )+c_{1} \\ y \left (x \right ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 28
DSolve[x (y'[x])^2+(1-x^2 y[x])y'[x]-x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to -\log (x)+c_1 \\ \end{align*}