74.1.55 problem 76

Internal problem ID [15756]
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 : 76
Date solved : Thursday, March 13, 2025 at 06:17:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+153 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 22

ode:=16*diff(diff(y(x),x),x)+24*diff(y(x),x)+153*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {3 x}{4}} \left (c_{1} \sin \left (3 x \right )+c_{2} \cos \left (3 x \right )\right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 28

ode=16*D[y[x],{x,2}]+24*D[y[x],x]+153*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x/4} (c_2 \cos (3 x)+c_1 \sin (3 x)) \]

✓ Sympy. Time used: 0.179 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(153*y(x) + 24*Derivative(y(x), x) + 16*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )}\right ) e^{- \frac {3 x}{4}} \]