10.2.21 problem 21

Internal problem ID [1149]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 21
Date solved : Saturday, March 29, 2025 at 10:42:23 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.167 (sec). Leaf size: 107

ode:=diff(y(x),x) = (3*x^2+1)/(-6*y(x)+3*y(x)^2); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\left (1+i \sqrt {3}\right ) \left (4 x^{3}+4 x +4 \sqrt {x^{6}+2 x^{4}+x^{2}-4}\right )^{{2}/{3}}-4 i \sqrt {3}-4 \left (4 x^{3}+4 x +4 \sqrt {x^{6}+2 x^{4}+x^{2}-4}\right )^{{1}/{3}}+4}{4 \left (4 x^{3}+4 x +4 \sqrt {x^{6}+2 x^{4}+x^{2}-4}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 4.061 (sec). Leaf size: 158

ode=D[y[x],x] == (3*x^2+1)/(-6*y[x]+3*y[x]^2); 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-i 2^{2/3} \sqrt {3} \left (x^3+\sqrt {x^6+2 x^4+x^2-4}+x\right )^{2/3}-2^{2/3} \left (x^3+\sqrt {x^6+2 x^4+x^2-4}+x\right )^{2/3}+4 \sqrt [3]{x^3+\sqrt {x^6+2 x^4+x^2-4}+x}+2 i \sqrt [3]{2} \sqrt {3}-2 \sqrt [3]{2}}{4 \sqrt [3]{x^3+\sqrt {x^6+2 x^4+x^2-4}+x}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x**2 - 1)/(3*y(x)**2 - 6*y(x)) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

ZeroDivisionError : polynomial division