Internal problem ID [6152]
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]
\[ \boxed {y^{\prime } y^{2}=x +2} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 18
dsolve([y(x)^2*diff(y(x),x)=x+2,y(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (12 x^{2}+48 x +512\right )^{\frac {1}{3}}}{2} \]
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 21
DSolve[{y[x]^2*y'[x]==x+2,{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt [3]{\frac {3 x^2}{2}+6 x+64} \]