Q. 54.1( 33 Votes )
For each of the differential equations given in question, find the general solution:
Answer :
It is given that 
This is equation in the form of 
(where, p = 
and Q =
)
Now, I.F. = 
Thus, the solution of the given differential equation is given by the relation:
y(I.F.) = 
-----------(1)
Now, Let t = tanx
⇒ sec2xdx = dt
Thus, the equation (1) becomes,
⇒ tetanx = (t – 1)et + C
⇒ tetanx = (tanx – 1)etanx + C
⇒ y = (tanx -1) + C e-tanx
Therefore, the required general solution of the given differential equation is
y = (tanx -1) + C e-tanx.
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