74.15.46 problem 49

Internal problem ID [16414]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 49
Date solved : Monday, March 31, 2025 at 02:52:44 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)+37*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \sin \left (6 \ln \left (x \right )\right )+c_3 \cos \left (6 \ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 60.082 (sec). Leaf size: 39

ode=x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]+37*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\frac {c_2 \cos (6 \log (K[1]))+c_1 \sin (6 \log (K[1]))}{K[1]}dK[1]+c_3 \]

✓ Sympy. Time used: 0.187 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 3*x**2*Derivative(y(x), (x, 2)) + 37*x*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (6 \log {\left (x \right )} \right )} + C_{3} \cos {\left (6 \log {\left (x \right )} \right )} \]