Internal problem ID [2286]
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 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-12 \,{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+9*diff(y(x),x)=12*exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (3 x c_{1}+18 x^{2}-c_{1}+3 c_{2}-12 x +4\right ) {\mathrm e}^{3 x}}{9}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 37
DSolve[y'''[x]-6*y''[x]+9*y'[x]==12*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} e^{3 x} (3 x (6 x-4+c_2)+4+3 c_1-c_2)+c_3 \\ \end{align*}