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=et
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