77.1.53 problem 72 (page 112)

Internal problem ID [17943]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 72 (page 112)
Date solved : Tuesday, January 28, 2025 at 11:14:35 AM
CAS classification : [_quadrature]

\begin{align*} y&={\mathrm e}^{y^{\prime }} {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.319 (sec). Leaf size: 38

dsolve(y(x)=exp(diff(y(x),x))*diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \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: 0.322 (sec). Leaf size: 102

DSolve[y[x]==Exp[D[y[x],x]]*D[y[x],x]^2,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*}