Internal problem ID [2743]
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 41.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y=24 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)+diff(y(x),x$2)-10*diff(y(x),x)+8*y(x)=24*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (5 c_{3} {\mathrm e}^{6 x}+5 c_{1} {\mathrm e}^{5 x}+6 \,{\mathrm e}^{x}+5 c_{2} \right ) {\mathrm e}^{-4 x}}{5} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 37
DSolve[y'''[x]+y''[x]-10*y'[x]+8*y[x]==24*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {6 e^{-3 x}}{5}+c_1 e^{-4 x}+c_2 e^x+c_3 e^{2 x} \]