Internal problem ID [1179]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y-{\mathrm e}^{x} x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-x*(x+4)*diff(y(x),x)+2*(x+3)*y(x)=x^4*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} x^{2} {\mathrm e}^{x}+x^{2} c_{1}+{\mathrm e}^{x} x^{3} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 21
DSolve[x^2*y''[x]-x*(x+4)*y'[x]+2*(x+3)*y[x]==x^4*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (e^x (x-1+c_2)+c_1\right ) \\ \end{align*}