20.9.1 problem Problem 1

Internal problem ID [3745]
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 8.7, The Variation of Parameters Method. page 556
Problem number : Problem 1
Date solved : Monday, January 27, 2025 at 07:58:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=4*exp(3*x)*ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (2 \ln \left (x \right ) x^{2}+c_{1} x -3 x^{2}+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==4*Exp[3*x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (-3 x^2+2 x^2 \log (x)+c_2 x+c_1\right ) \]