82.11.3 problem Ex. 3

Internal problem ID [18692]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 28
Problem number : Ex. 3
Date solved : Monday, March 31, 2025 at 05:57:55 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=3 x^{2} y^{{1}/{3}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ y^{{2}/{3}}-\frac {6 x^{3}}{13}-\frac {c_1}{x^{{4}/{3}}} = 0 \]

✓ Mathematica. Time used: 9.778 (sec). Leaf size: 33

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

\[ y(x)\to \frac {\left (6 x^3+\frac {13 c_1}{x^{4/3}}\right ){}^{3/2}}{13 \sqrt {13}} \]

✓ Sympy. Time used: 1.976 (sec). Leaf size: 49

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {13} \left (\frac {C_{1}}{x^{\frac {4}{3}}} + 6 x^{3}\right )^{\frac {3}{2}}}{169}, \ y{\left (x \right )} = \frac {\sqrt {13} \left (\frac {C_{1}}{x^{\frac {4}{3}}} + 6 x^{3}\right )^{\frac {3}{2}}}{169}\right ] \]