Internal problem ID [1486]
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 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = -3, y^{\prime \prime }\relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([8*diff(y(x),x$3)-4*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0) = 4, D(y)(0) = -3, (D@@2)(y)(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = \left (1-2 x \right ) {\mathrm e}^{\frac {x}{2}}+3 \,{\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 56
DSolve[{8*y'''[x]-4*y''[x]-2*y'[x]-2*y[x]==0,{y[0]==4,y'[0]==-3,y''[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{21} e^{-x/4} \left (51 \cos \left (\frac {\sqrt {3} x}{4}\right )-13 \sqrt {3} \sin \left (\frac {\sqrt {3} x}{4}\right )\right )-\frac {6 e^x}{7} \\ \end{align*}