Internal problem ID [5596]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC
OSCILLATORS Page 98
Problem number: 2.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+{\mathrm e}^{x} \sin \relax (x ) c_{2}+c_{3} {\mathrm e}^{x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[y'''[x]-3*y''[x]+4*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 \cos (x)+c_1 \sin (x)+c_3) \\ \end{align*}