Internal problem ID [2222]
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 29.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-18*diff(y(x),x)-40*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{4 x}+c_{3} {\mathrm e}^{-5 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y'''[x]+3*y''[x]-18*y'[x]-40*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-5 x} \left (c_2 e^{3 x}+c_3 e^{9 x}+c_1\right ) \\ \end{align*}