Internal problem ID [6349]
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]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +{\mathrm e}^{x} \sin \left (x \right ) c_{2} +c_{3} {\mathrm e}^{x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 22
DSolve[y'''[x]-3*y''[x]+4*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (c_2 \cos (x)+c_1 \sin (x)+c_3) \]