Internal problem ID [1167]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (1+2 x \right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y-\left (1+2 x \right )^{2} {\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 26
dsolve((2*x+1)*diff(y(x),x$2)-2*diff(y(x),x)-(2*x+3)*y(x)=(2*x+1)^2*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+x \,{\mathrm e}^{x} c_{1}-\frac {\left (x +1\right ) x \,{\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 42
DSolve[(2*x+1)*y''[x]-2*y'[x]-(2*x+3)*y[x]==(2*x+1)^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} e^{-x} x (x+1)+c_1 e^{-x-\frac {1}{2}}+c_2 e^{x+\frac {1}{2}} x \\ \end{align*}