Internal problem ID [7417]
Book: Second order enumerated odes
Section: section 1
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y=x^{3}+x^{2}+x +1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=1+x+x^2+x^3,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2} +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +x^{3}-2 x^{2}-x +6 \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 60
DSolve[y''[x]+y'[x]+y[x]==1+x+x^2+x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3-2 x^2-x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+6 \]