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

, given that

Given Differential Equation :

Formula :

i)

ii)

iii) 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, x²=t => 2x dx = dt

………

Substituting I in eq(2),

Therefore, general solution is

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

Substituting c in general solution,

Multiplying above equation by

Therefore, particular solution is