50.2.14 problem 2(d)

Internal problem ID [7820]
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)
Date solved : Monday, January 27, 2025 at 03:24:08 PM
CAS classification : [_separable]

\begin{align*} y^{2} y^{\prime }&=x +2 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 21

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

\[ y(x)\to \sqrt [3]{\frac {3 x^2}{2}+6 x+64} \]