60.1.493 problem 496

Internal problem ID [10507]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 496
Date solved : Monday, January 27, 2025 at 08:31:12 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.253 (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 &= x -\sqrt {2}\, a \\ y &= x +\sqrt {2}\, a \\ y &= 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 &= 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: 104.897 (sec). Leaf size: 35180

DSolve[-(a^2*(1 + D[y[x],x])^2) + (-x + y[x])^2*(1 + D[y[x],x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

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