Internal problem ID [6674]
Book: Second order enumerated odes
Section: section 1
Problem number: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-x^{2}-x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+y(x)=1+x+x^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+x^{2}+x -1 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[y''[x]+y[x]==1+x+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+x+c_1 \cos (x)+c_2 \sin (x)-1 \\ \end{align*}