Find a particular solution satisfying the given condition for each of the following differential equations.

, given that

Given Differential Equation :

Formula :

i)

ii)

iii)

iv)

v)

vi) 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,

Let, u=x² and v= tan x. sec x

………

………

Substituting I in eq(2),

Multiplying above equation by cos x,

Therefore, general solution is

For particular solution put y=1 and x=0 in above equation,

Substituting c in general solution,

Therefore, particular solution is