Internal problem ID [1482]
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 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-2 y^{\prime }-4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 6, y^{\prime }\relax (0) = 3, y^{\prime \prime }\relax (0) = 22] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve([diff(y(x),x$3)-2*diff(y(x),x)-4*y(x)=0,y(0) = 6, D(y)(0) = 3, (D@@2)(y)(0) = 22],y(x), singsol=all)
\[ y \relax (x ) = \left (2 \cos \relax (x )-3 \sin \relax (x )\right ) {\mathrm e}^{-x}+4 \,{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 27
DSolve[{y'''[x]-2*y'[x]-4*y[x]==0,{y[0]==6,y'[0]==3,y''[0]==22}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (4 e^{3 x}-3 \sin (x)+2 \cos (x)\right ) \\ \end{align*}