29.21.6 problem 582

Internal problem ID [5176]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 582
Date solved : Tuesday, March 04, 2025 at 08:24:04 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} x^{2} \left (4 x -3 y\right ) y^{\prime }&=\left (6 x^{2}-3 x y+2 y^{2}\right ) y \end{align*}

✓ Maple. Time used: 0.144 (sec). Leaf size: 44

ode:=x^2*(4*x-3*y(x))*diff(y(x),x) = (6*x^2-3*x*y(x)+2*y(x)^2)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ 2 \ln \left (\frac {y \left (x \right )}{x}\right )-\ln \left (\frac {x^{2}+y \left (x \right )^{2}}{x^{2}}\right )-\frac {3 \arctan \left (\frac {y \left (x \right )}{x}\right )}{2}-\ln \left (x \right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 43

ode=x^2(4 x-3 y[x])D[y[x],x]==(6 x^2-3 x y[x]+2 y[x]^2)y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [3 \arctan \left (\frac {y(x)}{x}\right )+2 \log \left (\frac {y(x)^2}{x^2}+1\right )-4 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.727 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(4*x - 3*y(x))*Derivative(y(x), x) - (6*x**2 - 3*x*y(x) + 2*y(x)**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\frac {x \left (\frac {x^{2}}{y^{2}{\left (x \right )}} + 1\right )}{y{\left (x \right )}} \right )} + \frac {3 \operatorname {atan}{\left (\frac {x}{y{\left (x \right )}} \right )}}{2} \]