Find the general solution for each of the following differential equations.
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
Dividing above equation by (1 + x2),
………eq(1)
Equation (1) is of the form
Where, and
Therefore, integrating factor is
Let (1 + x2) = f(x)
Therefore f’(x) = 2x
………
………
General solution is
………
Therefore general solution is