Internal problem ID [1479]
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 15.
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 \prime }+4 y^{\prime }-8 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = -2, y^{\prime \prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(x),x$3)-2*diff(y(x),x$2)+4*diff(y(x),x)-8*y(x)=0,y(0) = 2, D(y)(0) = -2, (D@@2)(y)(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {5 \,{\mathrm e}^{2 x}}{4}-\frac {9 \sin \left (2 x \right )}{4}+\frac {3 \cos \left (2 x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{y'''[x]-2*y''[x]+4*y'[x]-8*y[x]==0,{y[0]==2,y'[0]==-2,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x}-2 \sin (2 x)+\cos (2 x) \\ \end{align*}