66.1.50 problem Problem 64

Internal problem ID [13897]
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 64
Date solved : Tuesday, January 28, 2025 at 06:07:55 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 20

dsolve(diff(y(x),x)^2+(x+a)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\left (a +x \right )^{2}}{4} \\ y &= c_{1} \left (c_{1} +a +x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 (a+x+c_1) \\ y(x)\to -\frac {1}{4} (a+x)^2 \\ \end{align*}