20.4.24 problem Problem 40

Internal problem ID [3659]
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 40
Date solved : Sunday, March 30, 2025 at 02:02:27 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \end{align*}

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

ode:=diff(y(x),x)-3/2*y(x)/x = 6*y(x)^(1/3)*x^2*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ -2 x^{3} \ln \left (x \right )+x^{3}+y^{{2}/{3}}-c_1 x = 0 \]

✓ Mathematica. Time used: 0.836 (sec). Leaf size: 26

ode=D[y[x],x]-3/(2*x)*y[x]==6*y[x]^(1/3)*x^2*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \left (x \left (-x^2+2 x^2 \log (x)+c_1\right )\right ){}^{3/2} \]

✓ Sympy. Time used: 2.704 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**2*y(x)**(1/3)*log(x) + Derivative(y(x), x) - 3*y(x)/(2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \left (x \left (C_{1} + 2 x^{2} \log {\left (x \right )} - x^{2}\right )\right )^{\frac {3}{2}}, \ y{\left (x \right )} = \left (x \left (C_{1} + 2 x^{2} \log {\left (x \right )} - x^{2}\right )\right )^{\frac {3}{2}}\right ] \]