65.8.15 problem 7 (b)

Internal problem ID [15736]
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 (b)
Date solved : Thursday, October 02, 2025 at 10:24:39 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 )&={\frac {1}{2}} \\ \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 15

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

\[ y = \frac {\sqrt {-4 x^{3}-3}}{2} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \frac {1}{2} \sqrt {-4 x^3-3} \end{align*}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 14

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): 1/2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {- x^{3} - \frac {3}{4}} \]