74.2.4 problem 9

Internal problem ID [15845]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 08:09:22 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+45 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+45*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} \left (c_{1} \sin \left (6 x \right )+c_{2} \cos \left (6 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+45*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} (c_2 \cos (6 x)+c_1 \sin (6 x)) \]