81.3.28 problem 28

Internal problem ID [18567]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 28
Date solved : Thursday, March 13, 2025 at 12:22:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} 3 x^{2} y^{\prime }+2 x^{2}-3 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 26

ode:=3*x^2*diff(y(x),x)+2*x^2-3*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {x \left (\sqrt {33}-11 \tanh \left (\frac {\left (\ln \left (x \right )+c_{1} \right ) \sqrt {33}}{6}\right )\right ) \sqrt {33}}{66} \]

✓ Mathematica. Time used: 2.278 (sec). Leaf size: 101

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

\begin{align*} y(x)\to -\frac {x \left (\left (\sqrt {33}-3\right ) e^{\sqrt {33} c_1} x^{\sqrt {\frac {11}{3}}}-\sqrt {33}-3\right )}{6+6 e^{\sqrt {33} c_1} x^{\sqrt {\frac {11}{3}}}} \\ y(x)\to -\frac {1}{6} \left (\sqrt {33}-3\right ) x \\ y(x)\to \frac {1}{6} \left (3+\sqrt {33}\right ) x \\ \end{align*}

✓ Sympy. Time used: 0.293 (sec). Leaf size: 41

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

\[ y{\left (x \right )} = \frac {x \left (C_{1} \left (3 + \sqrt {33}\right ) + x^{\frac {\sqrt {33}}{3}} \left (-3 + \sqrt {33}\right )\right )}{6 \left (C_{1} - x^{\frac {\sqrt {33}}{3}}\right )} \]