20.10.6 problem Problem 19

Internal problem ID [3778]
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
Date solved : Monday, January 27, 2025 at 08:02:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y&=4 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.052 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+6*x*D[y[x],x]+6*y[x]==4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{2 x} (x-1)+c_2 x+c_1}{x^3} \]