74.1.17 problem 24

Internal problem ID [15797]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:07:34 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+40 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-12*diff(y(x),x)+40*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,2}]-12*D[y[x],x]+40*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{6 x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \]