26.1.3 problem 1.c

Internal problem ID [4243]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.c
Date solved : Tuesday, March 04, 2025 at 05:58:45 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 12

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

\[ y \left (x \right ) = \tan \left (c_{1} x^{3}\right ) x \]

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 37

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{\text {Arctan}(K[1]) \left (K[1]^2+1\right )}dK[1]=3 \log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.077 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = x \tan {\left (C_{1} x^{3} \right )} \]