15.8.47 problem 50

Internal problem ID [3050]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 50
Date solved : Sunday, March 30, 2025 at 01:14:10 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 1.010 (sec). Leaf size: 45

ode:=3*x*y(x)+(3*x^2+y(x)^2)*diff(y(x),x) = 0; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-3 x^{2}+\sqrt {9 x^{4}+1}} \\ y &= -i \sqrt {3 x^{2}-\sqrt {9 x^{4}+1}} \\ \end{align*}

✓ Mathematica. Time used: 9.022 (sec). Leaf size: 26

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

\[ y(x)\to \sqrt {\sqrt {9 x^4+1}-3 x^2} \]

✓ Sympy. Time used: 3.972 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \sqrt {- 3 x^{2} + \sqrt {9 x^{4} + 1}} \]