83.4.7 problem 7

Internal problem ID [19008]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 7
Date solved : Monday, March 31, 2025 at 06:31:46 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 10

ode:=diff(y(x),x) = y(x)/x+tan(y(x)/x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (c_1 x \right ) x \]

✓ Mathematica. Time used: 3.053 (sec). Leaf size: 19

ode=D[y[x],x]==y[x]/x+Tan[y[x]/x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x \arcsin \left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.079 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = x \left (\pi - \operatorname {asin}{\left (C_{1} x \right )}\right ), \ y{\left (x \right )} = x \operatorname {asin}{\left (C_{1} x \right )}\right ] \]