74.2.19 problem 24

Internal problem ID [15860]
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 : Tuesday, January 28, 2025 at 08:10:30 AM
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*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 14

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

\[ y(x)\to \sqrt [3]{x-3} x \]