5.14 problem 25

Internal problem ID [4296]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number: 25.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(x),x$3)+diff(y(x),x$2)-6*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-3 x} \]

Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 30

DSolve[y'''[x]+y''[x]-6*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{3} c_1 e^{-3 x}+\frac {1}{2} c_2 e^{2 x}+c_3 \\ \end{align*}