Internal problem ID [8076]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 496.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y-x \right )^{2} \left (\left (y^{\prime }\right )^{2}+1\right )-a^{2} \left (y^{\prime }+1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 130
dsolve((y(x)-x)^2*(diff(y(x),x)^2+1)-a^2*(diff(y(x),x)+1)^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: 52.048 (sec). Leaf size: 18407
DSolve[-(a^2*(1 + y'[x])^2) + (-x + y[x])^2*(1 + y'[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display