Internal problem ID [2742]
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]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y=4 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
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)
\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{4 x}+3 c_{1} {\mathrm e}^{3 x}+3 c_{3} {\mathrm e}^{x}+3 c_{2} \right ) {\mathrm e}^{-2 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 37
DSolve[y'''[x]+2*y''[x]-y'[x]-2*y[x]==4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{2 x}}{3}+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^x \]