83.4.11 problem 11

Internal problem ID [19012]
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 : 11
Date solved : Monday, March 31, 2025 at 06:32:34 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 11

ode:=x*sin(y(x)/x)*diff(y(x),x) = y(x)*sin(y(x)/x)-x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arccos \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.402 (sec). Leaf size: 30

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

\begin{align*} y(x)\to -x \arccos (\log (x)-c_1) \\ y(x)\to x \arccos (\log (x)-c_1) \\ \end{align*}

✓ Sympy. Time used: 0.897 (sec). Leaf size: 24

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

\[ \left [ y{\left (x \right )} = x \left (- \operatorname {acos}{\left (C_{1} + \log {\left (x \right )} \right )} + 2 \pi \right ), \ y{\left (x \right )} = x \operatorname {acos}{\left (C_{1} + \log {\left (x \right )} \right )}\right ] \]