Internal problem ID [14124]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {4 x -9}{3 \left (x -3\right )^{\frac {2}{3}}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x \left (-3+x \right )^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 14
DSolve[{y'[x]==1/3*(4*x-9)*(x-3)^(-2/3),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt [3]{x-3} x \]