Internal problem ID [222]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+4 y^{\prime }+y-3 \,{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 27
dsolve(4*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=3*x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} c_{2}+{\mathrm e}^{-\frac {x}{2}} x c_{1}+\frac {\left (3 x -4\right ) {\mathrm e}^{x}}{9} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 33
DSolve[4*y''[x]+4*y'[x]+y[x]==3*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} e^x (3 x-4)+e^{-x/2} (c_2 x+c_1) \\ \end{align*}