Internal problem ID [1477]
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 13.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+3 y^{\prime \prime }-13 y^{\prime }-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(4*diff(y(x),x$4)+12*diff(y(x),x$3)+3*diff(y(x),x$2)-13*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{-\frac {3 x}{2}}+c_{3} {\mathrm e}^{x}+c_{4} {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 41
DSolve[4*y''''[x]+12*y'''[x]+3*y''[x]-13*y'[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{x/2} \left (c_2 e^x+c_4 e^{5 x/2}+c_1\right )+c_3\right ) \\ \end{align*}