Internal problem ID [7405]
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]]
\[ \boxed {{y^{\prime \prime }}^{2}+y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)^2+diff(y(x),x)=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} +x y \left (x \right ) = -\frac {1}{12} x^{3}+\frac {1}{2} x^{2} c_{1} -c_{1}^{2} x +x +c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 67
DSolve[(y''[x])^2+y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^3}{12}-\frac {c_1 x^2}{4}+x-\frac {c_1{}^2 x}{4}+c_2 y(x)\to -\frac {x^3}{12}+\frac {c_1 x^2}{4}+x-\frac {c_1{}^2 x}{4}+c_2 \end{align*}