Find the general solution for each of the following differential equations.


Given Differential Equation :



Formula :


i)


ii)


iii)


iv)


v) General solution :


For the differential equation in the form of



General solution is given by,



Where, integrating factor,



Answer :


Given differential equation is


………eq(1)


Equation (1) is of the form



Where, and


Therefore, integrating factor is




………


………


………



General solution is



………eq(2)


Let,



Put, cos x=t => -sin x dx = dt



………



Substituting I in eq(2),



Multiplying above equation by cos2x,



Therefore, general solution is



1