Internal problem ID [15094]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 206.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{2}-y y^{\prime }=-{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 34
dsolve(diff(y(x),x)^2-y(x)*diff(y(x),x)+exp(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \,{\mathrm e}^{\frac {x}{2}} \\ y \left (x \right ) &= 2 \,{\mathrm e}^{\frac {x}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{x} c_{1}^{2}+1}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.203 (sec). Leaf size: 59
DSolve[y'[x]^2-y[x]*y'[x]+Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-e^{-c_1} \left (-e^x+e^{c_1}\right ){}^2} \\ y(x)\to \sqrt {-e^{-c_1} \left (e^x-e^{c_1}\right ){}^2} \\ \end{align*}