10.5.23 problem 30

Internal problem ID [1215]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 30
Date solved : Thursday, March 13, 2025 at 03:55:26 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

\[ x^{4}+y^{4}+3 x y+c_1 = 0 \]

✓ Mathematica. Time used: 60.161 (sec). Leaf size: 1181

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out