Internal problem ID [2298]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with
Nonconstant Coefficients. page 567
Problem number: Problem 19.
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 }+6 y^{\prime } x +6 y-4 \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(x^2*diff(y(x),x$2)+6*x*diff(y(x),x)+6*y(x)=4*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\frac {c_{1}}{x}-\frac {{\mathrm e}^{2 x}}{x}+{\mathrm e}^{2 x}+c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 25
DSolve[x^2*y''[x]+6*x*y'[x]+6*y[x]==4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 x} (x-1)+c_2 x+c_1}{x^3} \\ \end{align*}