Internal problem ID [15096]
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: 208.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-{y^{\prime }}^{2} {\mathrm e}^{y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 38
dsolve(y(x)=diff(y(x),x)^2*exp(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (x -c_{1} \right ) \left (\operatorname {LambertW}\left (\left (x -c_{1} \right ) {\mathrm e}\right )-1\right )^{2}}{\operatorname {LambertW}\left (\left (x -c_{1} \right ) {\mathrm e}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 102
DSolve[y[x]==y'[x]^2*Exp[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1}}{W\left (-\frac {\sqrt {\text {$\#$1}}}{2}\right )}+\frac {\text {$\#$1}}{2 W\left (-\frac {\sqrt {\text {$\#$1}}}{2}\right )^2}\&\right ][2 x+c_1] \\ y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1}}{W\left (\frac {\sqrt {\text {$\#$1}}}{2}\right )}+\frac {\text {$\#$1}}{2 W\left (\frac {\sqrt {\text {$\#$1}}}{2}\right )^2}\&\right ][2 x+c_1] \\ y(x)\to 0 \\ \end{align*}