Internal problem ID [2284]
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 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y-36 \,{\mathrm e}^{2 x} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=36*exp(2*x)*ln(x),y(x), singsol=all)
\[ y \relax (x ) = 6 \ln \relax (x ) {\mathrm e}^{2 x} x^{3}-11 \,{\mathrm e}^{2 x} x^{3}+c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{2 x} x +c_{3} {\mathrm e}^{2 x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y'''[x]-6*y''[x]+12*y'[x]-8*y[x]==36*Exp[2*x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (6 x^3 \log (x)+x (x (-11 x+c_3)+c_2)+c_1\right ) \\ \end{align*}