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