Internal problem ID [1164]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y-4 \,{\mathrm e}^{-x \left (2+x \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2+2)*y(x)=4*exp(-x*(x+2)),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x^{2}} c_{2}+x \,{\mathrm e}^{-x^{2}} c_{1}+{\mathrm e}^{-x \left (2+x \right )} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 27
DSolve[4*x^2*y''[x]+(4*x-8*x^2)*y'[x]+(4*x^2-4*x-1)*y[x]==4*x^(1/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x (x \log (x)+(-1+c_2) x+c_1)}{\sqrt {x}} \\ \end{align*}