Internal problem ID [2998]
Book: Applied Differential equations, N Curle, 1971
Section: Examples, page 35
Problem number: 1.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-y^{\prime }-\frac {{y^{\prime }}^{2}}{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 145
dsolve(y(x)=diff(y(x),x)+1/2*(diff(y(x),x))^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {{\mathrm e}^{-2 \operatorname {LambertW}\left (-\sqrt {2}\, {\mathrm e}^{-c_{1} +x -1}\right )-2 c_{1} +2 x +\ln \left (2\right )-2}}{2}-{\mathrm e}^{-\operatorname {LambertW}\left (-{\mathrm e}^{-c_{1}} {\mathrm e}^{x} \sqrt {2}\, {\mathrm e}^{-1}\right )-c_{1} +x +\frac {\ln \left (2\right )}{2}-1} y \left (x \right ) = \frac {{\mathrm e}^{2 \operatorname {RootOf}\left (-\textit {\_Z} -2 x +2 \,{\mathrm e}^{\textit {\_Z}}-2+2 c_{1} +\ln \left (\frac {{\mathrm e}^{3 \textit {\_Z}}}{2}-2 \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}}\right )\right )}}{2}-{\mathrm e}^{\operatorname {RootOf}\left (-\textit {\_Z} -2 x +2 \,{\mathrm e}^{\textit {\_Z}}-2+2 c_{1} +\ln \left (\frac {{\mathrm e}^{3 \textit {\_Z}}}{2}-2 \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}}\right )\right )} \end{align*}
✓ Solution by Mathematica
Time used: 18.04 (sec). Leaf size: 66
DSolve[y[x]==y'[x]+1/2*(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} W\left (-e^{x-1-c_1}\right ) \left (2+W\left (-e^{x-1-c_1}\right )\right ) y(x)\to \frac {1}{2} W\left (e^{x-1+c_1}\right ) \left (2+W\left (e^{x-1+c_1}\right )\right ) y(x)\to 0 \end{align*}