Internal problem ID [2265]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y-4 \,{\mathrm e}^{3 x} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=4*exp(3*x)*ln(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+x \,{\mathrm e}^{3 x} c_{1}+{\mathrm e}^{3 x} x^{2} \left (2 \ln \relax (x )-3\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 29
DSolve[y''[x]-6*y'[x]+9*y[x]==4*Exp[3*x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x} \left (2 x^2 \log (x)+x (-3 x+c_2)+c_1\right ) \\ \end{align*}