Internal problem ID [4178]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 944.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y {y^{\prime }}^{2}+2 a x y^{\prime }-a y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 115
dsolve(y(x)*diff(y(x),x)^2+2*a*x*diff(y(x),x)-a*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = x \sqrt {-a} y \left (x \right ) = -x \sqrt {-a} y \left (x \right ) = 0 y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}+\sqrt {a \,\textit {\_a}^{2}+a^{2}}+a}{\textit {\_a} \left (\textit {\_a}^{2}+a \right )}d \textit {\_a} \right )+c_{1} \right ) x y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {\textit {\_a}^{2}-\sqrt {a \left (\textit {\_a}^{2}+a \right )}+a}{\textit {\_a} \left (\textit {\_a}^{2}+a \right )}d \textit {\_a} +c_{1} \right ) x \end{align*}
✓ Solution by Mathematica
Time used: 8.189 (sec). Leaf size: 88
DSolve[y[x] (y'[x])^2+2 a x y'[x]-a y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {e^{c_1} \left (-2 \sqrt {a} x+e^{c_1}\right )} y(x)\to \sqrt {e^{c_1} \left (-2 \sqrt {a} x+e^{c_1}\right )} y(x)\to 0 y(x)\to -i \sqrt {a} x y(x)\to i \sqrt {a} x \end{align*}