77.43.10 problem Ex 11 page 13

Internal problem ID [20802]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 11 page 13
Date solved : Thursday, October 02, 2025 at 06:25:15 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \cos \left (x \right ) c_1 +\sin \left (x \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \sin (x)+c_1 \cos (x) \end{align*}

✓ Sympy. Time used: 0.416 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} \cos {\left (x \right )} + \sin {\left (x \right )} \]