83.5.6 problem 6

Internal problem ID [19022]
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 (D) at page 16
Problem number : 6
Date solved : Thursday, March 13, 2025 at 01:23:31 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=sin(x)*cos(x)*diff(y(x),x) = y(x)+sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \left (\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )-c_{1} \right ) \left (-\csc \left (2 x \right )+\cot \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 16

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

\[ y(x)\to \tan (x) (-\text {arctanh}(\cos (x))+c_1) \]

✗ Sympy

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

Timed Out