Internal problem ID [3622]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 894.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-\left (x -y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x)^2 = (x-y(x))^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\ln \relax (x )+c_{1}\right ) x \\ y \relax (x ) = \frac {x}{2}+\frac {c_{1}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 30
DSolve[x^2 (y'[x])^2==(x-y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{2}+\frac {c_1}{x} \\ y(x)\to x (-\log (x)+c_1) \\ \end{align*}