Internal problem ID [1484]
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 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1, y^{\prime \prime }\relax (0) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 19
dsolve([diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=0,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = -4],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} \left (2 x^{2}-3 x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{y'''[x]-6*y''[x]+12*y'[x]-8*y[x]==0,{y[0]==1,y'[0]==-1,y''[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} (x-1) (2 x-1) \\ \end{align*}