Internal problem ID [8831]
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]
\[ \boxed {\left (y-x \right )^{2} \left ({y^{\prime }}^{2}+1\right )-a^{2} \left (y^{\prime }+1\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.36 (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 \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: 50.68 (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]
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