77.3.7 problem 7

Internal problem ID [20348]
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 (B) at page 9
Problem number : 7
Date solved : Thursday, October 02, 2025 at 05:44:36 PM
CAS classification : [_separable]

\begin{align*} \left (3+2 \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime }&=1+2 \sin \left (y\right )+\cos \left (y\right ) \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 22

ode:=(3+2*sin(x)+cos(x))*diff(y(x),x) = 1+2*sin(y(x))+cos(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 \arctan \left (\frac {{\mathrm e}^{2 \arctan \left (1+\tan \left (\frac {x}{2}\right )\right )} c_1}{2}-\frac {1}{2}\right ) \]

✓ Mathematica. Time used: 60.302 (sec). Leaf size: 509

ode=(3+2*Sin[x]+Cos[x])*D[y[x],x]==1+2*Sin[y[x]]+Cos[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.730 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*sin(x) + cos(x) + 3)*Derivative(y(x), x) - 2*sin(y(x)) - cos(y(x)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 \operatorname {atan}{\left (C_{1} e^{2 \operatorname {atan}{\left (\tan {\left (\frac {x}{2} \right )} + 1 \right )} + 2 \pi \left \lfloor {\frac {x}{2 \pi } - \frac {1}{2}}\right \rfloor } - \frac {1}{2} \right )} \]