44.2.14 problem 2(d)

Internal problem ID [9106]
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 : Tuesday, September 30, 2025 at 06:04:25 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*}

✓ Maple. Time used: 0.145 (sec). Leaf size: 18

ode:=y(x)^2*diff(y(x),x) = x+2; 
ic:=[y(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.143 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \sqrt [3]{\frac {3 x^2}{2}+6 x+64} \end{align*}

✓ Sympy. Time used: 1.045 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + y(x)**2*Derivative(y(x), x) - 2,0) 
ics = {y(0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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