15.4.21 problem 22

Internal problem ID [2934]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 22
Date solved : Sunday, March 30, 2025 at 12:58:38 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )}&=0 \end{align*}

✓ Maple. Time used: 0.200 (sec). Leaf size: 90

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

\begin{align*} y &= \operatorname {RootOf}\left (\textit {\_Z}^{8} x^{4} c_1^{4}-4 \textit {\_Z}^{5} \left (\frac {1}{x c_1}\right )^{{4}/{5}}-3 \left (\frac {1}{x c_1}\right )^{{4}/{5}}\right )^{{5}/{2}} x \\ y &= -\operatorname {RootOf}\left (\textit {\_Z}^{8} x^{4} c_1^{4}-4 \textit {\_Z}^{5} \left (\frac {1}{x c_1}\right )^{{4}/{5}}-3 \left (\frac {1}{x c_1}\right )^{{4}/{5}}\right )^{{5}/{2}} x \\ \end{align*}

✓ Mathematica. Time used: 60.157 (sec). Leaf size: 1649

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

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✓ Sympy. Time used: 0.823 (sec). Leaf size: 29

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

\[ \log {\left (x \right )} = C_{1} + \log {\left (\frac {\left (3 + \frac {4 y^{2}{\left (x \right )}}{x^{2}}\right )^{\frac {5}{24}}}{\left (\frac {y{\left (x \right )}}{x}\right )^{\frac {2}{3}}} \right )} \]