30.16 problem 875

Internal problem ID [3604]

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]

Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x=0} \end {gather*}

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 \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \\ y \relax (x ) = -\ln \relax (x )+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*}