2.14 problem 2(d)

Internal problem ID [5399]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number: 2(d).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{2} y^{\prime }-x -2=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4] \end {align*}

Solution by Maple

Time used: 0.078 (sec). Leaf size: 18

dsolve([y(x)^2*diff(y(x),x)=x+2,y(0) = 4],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\left (12 x^{2}+48 x +512\right )^{\frac {1}{3}}}{2} \]

Solution by Mathematica

Time used: 0.321 (sec). Leaf size: 19

DSolve[{y[x]^2*y'[x]==x+2,{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt [3]{\frac {3}{2} x (x+4)+64} \\ \end{align*}