50.13.1 problem 1

Internal problem ID [8016]
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 : 1
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 }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +{\mathrm e}^{2 x} c_{2} +c_3 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

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

\[ y(x)\to c_1 e^x+\frac {1}{2} c_2 e^{2 x}+c_3 \]