Internal problem ID [1480]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient.
Page 483
Problem number: section 9.2, problem 16.
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 }-y^{\prime }-3 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 14, y^{\prime \prime }\relax (0) = -40] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve([diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=0,y(0) = 0, D(y)(0) = 14, (D@@2)(y)(0) = -40],y(x), singsol=all)
\[ y \relax (x ) = \left (2 \,{\mathrm e}^{4 x}+3 \,{\mathrm e}^{2 x}-5\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[{y'''[x]+3*y''[x]-y'[x]-3*y[x]==0,{y[0]==0,y'[0]==14,y''[0]==-40}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -5 e^{-3 x}+3 e^{-x}+2 e^x \\ \end{align*}