Internal problem ID [12138]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 39.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {y-5 y^{\prime } x +{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 93
dsolve(y(x)=5*x*diff(y(x),x)-diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} -\frac {4 \sqrt {2}\, c_{1}}{\left (10 x -2 \sqrt {25 x^{2}-4 y \left (x \right )}\right )^{\frac {5}{4}}}+\frac {4 x}{9}+\frac {\sqrt {25 x^{2}-4 y \left (x \right )}}{9} &= 0 \\ -\frac {4 \sqrt {2}\, c_{1}}{\left (10 x +2 \sqrt {25 x^{2}-4 y \left (x \right )}\right )^{\frac {5}{4}}}+\frac {4 x}{9}-\frac {\sqrt {25 x^{2}-4 y \left (x \right )}}{9} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.449 (sec). Leaf size: 2233
DSolve[y[x]==5*x*y'[x]-y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
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