20.4.29 problem Problem 45

Internal problem ID [3664]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 45
Date solved : Sunday, March 30, 2025 at 02:02:45 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(y(x),x)+6*y(x)/x = 3/x*y(x)^(2/3)*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {y^{{1}/{3}} x^{2}-x \sin \left (x \right )-\cos \left (x \right )-c_1}{x^{2}} = 0 \]

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 20

ode=D[y[x],x]+6/x*y[x]==3/x*y[x]^(2/3)*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.665 (sec). Leaf size: 110

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 3*y(x)**(2/3)*cos(x)/x + 6*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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