29.33.27 problem 990

Internal problem ID [5566]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 990
Date solved : Monday, January 27, 2025 at 12:03:51 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.353 (sec). Leaf size: 135

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 (-2 x -\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}-2 a^{2}+\sqrt {-\textit {\_a}^{4}+2 \textit {\_a}^{2} a^{2}}}{\textit {\_a}^{2}-2 a^{2}}d \textit {\_a} +2 c_{1} \right ) \\ y \left (x \right ) &= x +\operatorname {RootOf}\left (-2 x +\int _{}^{\textit {\_Z}}-\frac {-2 a^{2}+\textit {\_a}^{2}-\sqrt {-\textit {\_a}^{4}+2 \textit {\_a}^{2} a^{2}}}{\textit {\_a}^{2}-2 a^{2}}d \textit {\_a} +2 c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 118.370 (sec). Leaf size: 35180

DSolve[(a^2-(x-y[x])^2)(D[y[x],x])^2+2 a^2 D[y[x],x]+a^2-(x-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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