Internal problem ID [7402]
Book: Second order enumerated odes
Section: section 1
Problem number: 13.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {{y^{\prime \prime }}^{2}+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)^2+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= -\frac {1}{12} x^{3}+\frac {1}{2} c_{1} x^{2}-x \,c_{1}^{2}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 69
DSolve[(y''[x])^2+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^3}{12}-\frac {1}{4} i c_1 x^2+\frac {c_1{}^2 x}{4}+c_2 \\ y(x)\to -\frac {x^3}{12}+\frac {1}{4} i c_1 x^2+\frac {c_1{}^2 x}{4}+c_2 \\ \end{align*}