Internal problem ID [1169]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (2+x \right ) y-6 \,{\mathrm e}^{x} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(x*diff(y(x),x$2)-(2*x+2)*diff(y(x),x)+(x+2)*y(x)=6*x^3*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} x^{3} c_{1}+\frac {3 \,{\mathrm e}^{x} x^{4}}{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 29
DSolve[x*y''[x]-(2*x+2)*y'[x]+(x+2)*y[x]==6*x^3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^x \left (9 x^4+2 c_2 x^3+6 c_1\right ) \\ \end{align*}