44.1.23 problem 25

Internal problem ID [6898]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:34:24 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

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

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