66.1.27 problem Problem 39

Internal problem ID [13874]
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
Date solved : Tuesday, January 28, 2025 at 06:06:38 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} y&=5 x y^{\prime }-{y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.116 (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}\right )^{{5}/{4}}}+\frac {4 x}{9}+\frac {\sqrt {25 x^{2}-4 y}}{9} &= 0 \\ -\frac {4 \sqrt {2}\, c_{1}}{\left (10 x +2 \sqrt {25 x^{2}-4 y}\right )^{{5}/{4}}}+\frac {4 x}{9}-\frac {\sqrt {25 x^{2}-4 y}}{9} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 41.801 (sec). Leaf size: 2238

DSolve[y[x]==5*x*D[y[x],x]-D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

Too large to display