Internal problem ID [6667]
Book: Second order enumerated odes
Section: section 1
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-x^{2}-x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+diff(y(x),x)=1+x+x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{3}-{\mathrm e}^{-x} c_{1}-\frac {x^{2}}{2}+2 x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 31
DSolve[y''[x]+y'[x]==1+x+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} x (x (2 x-3)+12)-c_1 e^{-x}+c_2 \\ \end{align*}