Internal problem ID [6656]
Book: Second order enumerated odes
Section: section 1
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (y^{\prime }\right )^{2}+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 61
dsolve(diff(y(x),x$2)+diff(y(x),x)^2+y(x)=0,y(x), singsol=all)
\begin{align*} \int _{}^{y \relax (x )}-\frac {2}{\sqrt {2+4 \,{\mathrm e}^{-2 \textit {\_a}} c_{1}-4 \textit {\_a}}}d \textit {\_a} -x -c_{2} = 0 \\ \int _{}^{y \relax (x )}\frac {2}{\sqrt {2+4 \,{\mathrm e}^{-2 \textit {\_a}} c_{1}-4 \textit {\_a}}}d \textit {\_a} -x -c_{2} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.43 (sec). Leaf size: 90
DSolve[y''[x]+(y'[x])^2+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {\sqrt {2}}{\sqrt {2 e^{-2 K[1]} c_1-2 K[1]+1}}dK[1]\&\right ][x+c_2] \\ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt {2}}{\sqrt {2 e^{-2 K[2]} c_1-2 K[2]+1}}dK[2]\&\right ][x+c_2] \\ \end{align*}