50.9.11 problem 1(k)

Internal problem ID [7947]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 1(k)
Date solved : Monday, January 27, 2025 at 03:33:38 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(4*diff(y(x),x$2)+20*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[4*D[y[x],{x,2}]+20*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-5 x/2} (c_2 x+c_1) \]