50.1.34 problem 7

Internal problem ID [7806]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 7
Date solved : Monday, January 27, 2025 at 03:23:34 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(2*diff(y(x),x$3)+diff(y(x),x$2)-5*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{3 x} c_{2} +c_3 \,{\mathrm e}^{\frac {5 x}{2}}+c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[2*D[y[x],{x,3}]+D[y[x],{x,2}]-5*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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