44.8.11 problem 2(c)

Internal problem ID [9213]
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. Problems for Review and Discovery. Page 53
Problem number : 2(c)
Date solved : Tuesday, September 30, 2025 at 06:14:49 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 15

ode:=y(x)^2*diff(y(x),x) = x; 
ic:=[y(-1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (12 x^{2}+204\right )^{{1}/{3}}}{2} \]

✓ Mathematica. Time used: 0.119 (sec). Leaf size: 22

ode=y[x]^2*D[y[x],x]==x; 
ic={y[-1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+17} \end{align*}

✓ Sympy. Time used: 0.933 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + y(x)**2*Derivative(y(x), x),0) 
ics = {y(-1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [3]{\frac {3 x^{2}}{2} + \frac {51}{2}} \]