Internal problem ID [2744]
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]]
\[ \boxed {y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }=6 \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {c_{1} {\mathrm e}^{-3 x}}{3}-\frac {c_{2} {\mathrm e}^{-2 x}}{2}-3 \,{\mathrm e}^{-x}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 37
DSolve[y'''[x]+5*y''[x]+6*y'[x]==6*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -3 e^{-x}-\frac {1}{3} c_1 e^{-3 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]