Internal problem ID [4222]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 990.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\left (a^{2}-\left (-y+x \right )^{2}\right ) {y^{\prime }}^{2}+2 y^{\prime } a^{2}-\left (-y+x \right )^{2}=-a^{2}} \]
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 130
dsolve((a^2-(x-y(x))^2)*diff(y(x),x)^2+2*a^2*diff(y(x),x)+a^2-(x-y(x))^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = x -\sqrt {2}\, a y \left (x \right ) = x +\sqrt {2}\, a y \left (x \right ) = x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}-\frac {\textit {\_a}^{2}-2 a^{2}+\sqrt {-\textit {\_a}^{2} \left (\textit {\_a}^{2}-2 a^{2}\right )}}{2 \left (\textit {\_a}^{2}-2 a^{2}\right )}d \textit {\_a} +c_{1} \right ) y \left (x \right ) = x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}-\frac {-2 a^{2}+\textit {\_a}^{2}-\sqrt {-\textit {\_a}^{2} \left (\textit {\_a}^{2}-2 a^{2}\right )}}{2 \left (\textit {\_a}^{2}-2 a^{2}\right )}d \textit {\_a} +c_{1} \right ) \end{align*}
✓ Solution by Mathematica
Time used: 51.486 (sec). Leaf size: 18407
DSolve[(a^2-(x-y[x])^2)(y'[x])^2+2 a^2 y'[x]+a^2-(x-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
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