Internal problem ID [1470]
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 6.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 22
dsolve(4*diff(y(x),x$3)-8*diff(y(x),x$2)+5*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{\frac {x}{2}}+c_{3} {\mathrm e}^{\frac {x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[4*y'''[x]-8*y''[x]+5*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x/2} (c_2 x+c_1)+c_3 e^x \\ \end{align*}