Internal problem ID [224]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+4 y^{\prime }+7 y-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(2*diff(y(x),x$2)+4*diff(y(x),x)+7*y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \sin \left (\frac {\sqrt {10}\, x}{2}\right ) c_{2}+{\mathrm e}^{-x} \cos \left (\frac {\sqrt {10}\, x}{2}\right ) c_{1}+\frac {x^{2}}{7}-\frac {8 x}{49}+\frac {4}{343} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 53
DSolve[2*y''[x]+4*y'[x]+7*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{343} (7 x (7 x-8)+4)+e^{-x} \left (c_2 \cos \left (\sqrt {\frac {5}{2}} x\right )+c_1 \sin \left (\sqrt {\frac {5}{2}} x\right )\right ) \\ \end{align*}