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)

vii)

viii) General solution :

For the differential equation in the form of

General solution is given by,

Where, integrating factor,

Answer :

Given differential equation is

Dividing above equation by x,

………eq(1)

Equation (1) is of the form

Where, and

Therefore, integrating factor is

………

………

………

General solution is

………eq(2)

Let,

Put, log x =t => x=e^t

Therefore, (1/x) dx = dt

Let, u=t and v=e^-t

………

………

………

Substituting I in eq(2),

Multiplying above equation by x,

Therefore, general solution is

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

………

Substituting c in general solution,

Therefore, particular solution is