84.15.8 problem 8.8

Internal problem ID [22180]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Solved problems. Page 33
Problem number : 8.8
Date solved : Thursday, October 02, 2025 at 08:33:33 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \end{align*}

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

ode:=diff(y(x),x)-3*y(x)/x = x^4*y(x)^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ y^{{2}/{3}}-\frac {2 x^{5}}{9}-c_1 \,x^{2} = 0 \]

✓ Mathematica. Time used: 0.625 (sec). Leaf size: 26

ode=D[y[x],x]-3/x*y[x]==x^4*y[x]^(1/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{27} \left (2 x^5+9 c_1 x^2\right ){}^{3/2} \end{align*}

✓ Sympy. Time used: 0.879 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*y(x)**(1/3) + Derivative(y(x), x) - 3*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {x^{3} \left (C_{1} + 2 x^{3}\right )^{\frac {3}{2}}}{27}, \ y{\left (x \right )} = \frac {x^{3} \left (C_{1} + 2 x^{3}\right )^{\frac {3}{2}}}{27}\right ] \]