50.1.32 problem 5

Internal problem ID [7804]
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 : 5
Date solved : Monday, January 27, 2025 at 03:23:31 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{4 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (c_2 e^{3 x}+c_1\right ) \]