Internal problem ID [4077]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.15, page 220.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(3*diff(y(x),x$3)+5*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x}{3}}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[3*y'''[x]+5*y''[x]+y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (c_1 e^{4 x/3}+c_3 x+c_2\right ) \\ \end{align*}