68.2.19 problem 24

Internal problem ID [17147]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 24
Date solved : Thursday, October 02, 2025 at 01:45:02 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 11

ode:=diff(y(x),x) = 1/3*(4*x-9)/(x-3)^(2/3); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left (x -3\right )^{{1}/{3}} x \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 14

ode=D[y[x],x]==1/3*(4*x-9)*(x-3)^(-2/3); 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt [3]{x-3} x \end{align*}

✓ Sympy. Time used: 0.389 (sec). Leaf size: 107

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (4*x - 9)/(3*(x - 3)**(2/3)),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {\begin {cases} - \frac {3 \sqrt [3]{2} \left (x - \frac {9}{4}\right ) \sqrt [3]{4 x - 12}}{2} - \frac {27 \sqrt [3]{2} \sqrt [3]{4 x - 12}}{8} & \text {for}\: \left |{x - \frac {9}{4}}\right | > \frac {3}{4} \\- \frac {3 \sqrt [3]{2} \sqrt [3]{12 - 4 x} \left (x - \frac {9}{4}\right ) e^{\frac {i \pi }{3}}}{2} - \frac {27 \sqrt [3]{2} \sqrt [3]{12 - 4 x} e^{\frac {i \pi }{3}}}{8} & \text {otherwise} \end {cases}}{3} \]