Internal problem ID [6650]
Book: Second order enumerated odes
Section: section 1
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (y^{\prime }\right )^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+diff(y(x),x)^2=1,y(x), singsol=all)
\[ y \relax (x ) = x +\ln \left (\frac {{\mathrm e}^{-2 x} c_{1}}{2}-\frac {c_{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.506 (sec). Leaf size: 46
DSolve[y''[x]+(y'[x])^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log \left (e^x\right )+\log \left (e^{2 x}+e^{2 c_1}\right )+c_2 \\ y(x)\to -\log \left (e^x\right )+\log \left (e^{2 x}\right )+c_2 \\ \end{align*}