Internal problem ID [2233]
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 8.1, General Theory for Linear
Differential Equations. page 502
Problem number: Problem 40.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y-4 \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 27
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=4*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{2 x}}{3}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 37
DSolve[y'''[x]+2*y''[x]-y'[x]-2*y[x]==4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 x}}{3}+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^x \\ \end{align*}