Internal problem ID [12161]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.062 (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 \left (x \right ) &= -\frac {\left (a +x \right )^{2}}{4} \\ y \left (x \right ) &= c_{1} \left (c_{1} +a +x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 26
DSolve[y'[x]^2+(x+a)*y'[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*}