Internal problem ID [2221]
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 28.
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 }-4 y^{\prime }-12 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-4*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[y'''[x]+3*y''[x]-4*y'[x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (c_2 e^x+c_3 e^{5 x}+c_1\right ) \\ \end{align*}