Internal problem ID [220]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 2.
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^{\prime }-2 y-3 x -4=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=3*x+4,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+c_{1} {\mathrm e}^{2 x}-\frac {3 x}{2}-\frac {5}{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y''[x]-y'[x]-2*y[x]==3*x+4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 x}{2}+c_1 e^{-x}+c_2 e^{2 x}-\frac {5}{4} \\ \end{align*}