10.2.22 problem 22

Internal problem ID [1150]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 22
Date solved : Saturday, March 29, 2025 at 10:42:26 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}}{-4+3 y^{2}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.155 (sec). Leaf size: 71

ode:=diff(y(x),x) = 3*x^2/(-4+3*y(x)^2); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\left (1+i \sqrt {3}\right ) \left (-108+108 x^{3}+12 \sqrt {81 x^{6}-162 x^{3}-687}\right )^{{2}/{3}}-48 i \sqrt {3}+48}{12 \left (-108+108 x^{3}+12 \sqrt {81 x^{6}-162 x^{3}-687}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 9.255 (sec). Leaf size: 137

ode=D[y[x],x]== 3*x^2/(-4+3*y[x]^2); 
ic=y[1]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-i \sqrt [3]{2} 3^{2/3} \left (9 x^3+\sqrt {81 x^6-162 x^3-687}-9\right )^{2/3}-\sqrt [3]{2} \sqrt [6]{3} \left (9 x^3+\sqrt {81 x^6-162 x^3-687}-9\right )^{2/3}-8 \sqrt {3}+24 i}{2\ 2^{2/3} 3^{5/6} \sqrt [3]{9 x^3+\sqrt {81 x^6-162 x^3-687}-9}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2/(3*y(x)**2 - 4) + Derivative(y(x), x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out