4.6.31 problem 31

Internal problem ID [1248]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 31
Date solved : Tuesday, September 30, 2025 at 04:31:37 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.917 (sec). Leaf size: 111

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

\[ y = \frac {\left (i \sqrt {3}-1\right ) {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{{2}/{3}}-x^{3} \left (i x^{3} \sqrt {3}+x^{3}+2 {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{{1}/{3}}\right )}{6 {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{{1}/{3}} x} \]

✓ Mathematica. Time used: 50.896 (sec). Leaf size: 136

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

\begin{align*} y(x)&\to \frac {i \left (\left (\sqrt {3}+i\right ) x^3-\left (\sqrt {3}-i\right ) x^3+\left (\sqrt {3}+i\right ) \sqrt [3]{-x^9-54 x^2+6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}}-\frac {\left (\sqrt {3}-i\right ) x^6}{\sqrt [3]{-x^9-54 x^2+6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}}}\right )}{6 x} \end{align*}

✗ Sympy

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

Timed Out