24.1.17 problem 4(b)

Internal problem ID [4206]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 4(b)
Date solved : Tuesday, March 04, 2025 at 05:55:55 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

ode:=diff(y(x),x)*cos(x)+y(x) = sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (-2 \sin \left (x \right )-2 \ln \left (\sin \left (x \right )-1\right )+c_{1} \right ) \left (\cos \left (x \right )-\sin \left (x \right )+1\right )}{\cos \left (x \right )+\sin \left (x \right )+1} \]

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 42

ode=Cos[x]*D[y[x],x]+y[x]==Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \left (-2 \sin (x)-4 \log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+c_1\right ) \]

✓ Sympy. Time used: 34.787 (sec). Leaf size: 100

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

\[ y{\left (x \right )} = \frac {\sqrt {\sin {\left (x \right )} - 1} \left (C_{1} - 2 \int \frac {\sqrt {\sin {\left (x \right )} + 1} \sin {\left (x \right )}}{\sqrt {\sin {\left (x \right )} - 1}}\, dx + \int \frac {\sqrt {\sin {\left (x \right )} + 1} y{\left (x \right )}}{\sqrt {\sin {\left (x \right )} - 1} \cos {\left (x \right )}}\, dx\right )}{\sqrt {\sin {\left (x \right )} - 1} \int \frac {\sqrt {\sin {\left (x \right )} + 1}}{\sqrt {\sin {\left (x \right )} - 1} \cos {\left (x \right )}}\, dx - \sqrt {\sin {\left (x \right )} + 1}} \]