Internal problem ID [4097]
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, problem 35, 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*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1, y^{\prime \prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 21
dsolve([3*diff(y(x),x$3)+5*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (9 \,{\mathrm e}^{\frac {4 x}{3}}+4 x -9\right ) {\mathrm e}^{-x}}{16} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[{3*y'''[x]+5*y''[x]+y'[x]-y[x]==0,{y[0]==0,y'[0]==1,y''[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} e^{-x} \left (4 x+9 e^{4 x/3}-9\right ) \\ \end{align*}