Internal problem ID [1485]
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 21.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime \prime }-11 y^{\prime \prime }+12 y^{\prime }+9 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 6, y^{\prime }\relax (0) = 3, y^{\prime \prime }\relax (0) = 13] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve([2*diff(y(x),x$3)-11*diff(y(x),x$2)+12*diff(y(x),x)+9*y(x)=0,y(0) = 6, D(y)(0) = 3, (D@@2)(y)(0) = 13],y(x), singsol=all)
\[ y \relax (x ) = \left (2-x \right ) {\mathrm e}^{3 x}+4 \,{\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[{2*y'''[x]-11*y''[x]+12*y'[x]+9*y[x]==0,{y[0]==6,y'[0]==3,y''[0]==13}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 4 e^{-x/2}-e^{3 x} (x-2) \\ \end{align*}