89.5.6 problem 6

Internal problem ID [24356]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:21:42 PM
CAS classification : [_linear]

\begin{align*} \left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=(3*x-1)*diff(y(x),x) = 6*y(x)-10*(3*x-1)^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\frac {2}{\left (3 x -1\right )^{{5}/{3}}}+c_1 \right ) \left (3 x -1\right )^{2} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 27

ode=(3*x-1)*D[y[x],x]== 6*y[x]-10*(3*x-1)^(1/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \sqrt [3]{3 x-1}+c_1 (1-3 x)^2 \end{align*}

✓ Sympy. Time used: 0.363 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*(3*x - 1)**(1/3) + (3*x - 1)*Derivative(y(x), x) - 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 9 C_{1} x^{2} - 6 C_{1} x + C_{1} + 2 \sqrt [3]{3 x - 1} \]