Internal problem ID [6649]
Book: Second order enumerated odes
Section: section 1
Problem number: 16.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {\left (y^{\prime \prime }\right )^{2}+y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.672 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)^2+diff(y(x),x)=1,y(x), singsol=all)
\begin{align*} y \relax (x ) = x +c_{1} \\ y \relax (x ) = -\frac {1}{12} x^{3}+\frac {1}{2} c_{1} x^{2}-c_{1}^{2} x +x +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 59
DSolve[(y''[x])^2+y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {1}{12} x \left (x^2+3 c_1 x+3 \left (-4+c_1{}^2\right )\right ) \\ y(x)\to c_2-\frac {1}{12} x \left (x^2-3 c_1 x+3 \left (-4+c_1{}^2\right )\right ) \\ \end{align*}