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]
\[ \boxed {\left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 135
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 (-2 x -\left (\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} \right )+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: 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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