Internal problem ID [2235]
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 42.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }-6 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x$3)+5*diff(y(x),x$2)+6*diff(y(x),x)=6*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-2 x} c_{1}}{2}-\frac {c_{2} {\mathrm e}^{-3 x}}{3}-3 \,{\mathrm e}^{-x}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 35
DSolve[y'''[x]+5*y''[x]+6*y'[x]==6*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{-3 x} \left (-3 e^x \left (6 e^x+c_2\right )-2 c_1\right )+c_3 \\ \end{align*}