Internal problem ID [2774]
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]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=4 \,{\mathrm e}^{3 x} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.027 (sec). Leaf size: 30
DSolve[y''[x]-6*y'[x]+9*y[x]==4*Exp[3*x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} \left (-3 x^2+2 x^2 \log (x)+c_2 x+c_1\right ) \]