Internal problem ID [3714]
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]
Solve \begin {gather*} \boxed {\left (a^{2}-\left (x -y\right )^{2}\right ) \left (y^{\prime }\right )^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.337 (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 \relax (x ) = x -\sqrt {2}\, a \\ y \relax (x ) = x +\sqrt {2}\, a \\ y \relax (x ) = x +\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 \relax (x ) = x +\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 \textit {\_a}^{2}-4 a^{2}}d \textit {\_a} +c_{1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 67.941 (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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