50.13.2 problem 2

Internal problem ID [8017]
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
Date solved : Monday, January 27, 2025 at 03:36:51 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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)
 

\[ y = {\mathrm e}^{x} \left (c_{1} +\sin \left (x \right ) c_{2} +c_3 \cos \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (c_2 \cos (x)+c_1 \sin (x)+c_3) \]