Internal problem ID [1180]
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: 26.
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 }-2 x \left (2+x \right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y-2 \,{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-2*x*(x+2)*diff(y(x),x)+(x^2+4*x+6)*y(x)=2*x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} x^{2} {\mathrm e}^{x}+{\mathrm e}^{x} x^{3} c_{1}+x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 21
DSolve[x^2*y''[x]-2*x*(x+2)*y'[x]+(x^2+4*x+6)*y[x]==2*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x x (1+x (c_2 x+c_1)) \\ \end{align*}