40.3.5 problem 23 (i)

Internal problem ID [6609]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (i)
Date solved : Sunday, March 30, 2025 at 11:12:14 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational]

\begin{align*} 4 x^{3} y^{3}+\frac {1}{x}+\left (3 x^{4} y^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.198 (sec). Leaf size: 37

ode:=4*x^3*y(x)^3+1/x+(3*x^4*y(x)^2-1/y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {7 c_1}{3}} 3^{{2}/{3}} x}{3 \left (-\frac {x^{7} {\mathrm e}^{-7 c_1}}{\operatorname {LambertW}\left (-3 x^{7} {\mathrm e}^{-7 c_1}\right )}\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 3.451 (sec). Leaf size: 108

ode=(4*x^3*y[x]^3+1/x)+(3*x^4*y[x]^2-1/y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{W\left (-3 e^{-3 c_1} x^7\right )}}{x^{4/3}} \\ y(x)\to -\frac {\sqrt [3]{W\left (-3 e^{-3 c_1} x^7\right )}}{\sqrt [3]{3} x^{4/3}} \\ y(x)\to -\frac {(-1)^{2/3} \sqrt [3]{W\left (-3 e^{-3 c_1} x^7\right )}}{\sqrt [3]{3} x^{4/3}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.713 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*y(x)**3 + (3*x**4*y(x)**2 - 1/y(x))*Derivative(y(x), x) + 1/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \frac {3 x^{4} y^{3}{\left (x \right )}}{7} - \log {\left (x \right )} + \frac {3 \log {\left (x^{\frac {4}{3}} y{\left (x \right )} \right )}}{7} = C_{1} \]