65.8.16 problem 7 (c)

Internal problem ID [15737]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 7 (c)
Date solved : Thursday, October 02, 2025 at 10:24:41 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-\frac {3 x^{2}}{2 y} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 27

ode:=diff(y(x),x) = -3/2*x^2/y(x); 
ic:=[y(-1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-x^{3}-1} \\ y &= -\sqrt {-x^{3}-1} \\ \end{align*}

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 33

ode=D[y[x],x]==-3*x^2/(2*y[x]); 
ic={y[-1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-x^3-1}\\ y(x)&\to \sqrt {-x^3-1} \end{align*}

✓ Sympy. Time used: 0.169 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - \sqrt {- x^{3} - 1}, \ y{\left (x \right )} = \sqrt {- x^{3} - 1}\right ] \]