Internal problem ID [2807]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y=4 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
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)
\[ y \left (x \right ) = \frac {\left (x -1\right ) {\mathrm e}^{2 x}+c_{2} x -c_{1}}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.056 (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]
\[ y(x)\to \frac {e^{2 x} (x-1)+c_2 x+c_1}{x^3} \]