For each of the differential equations given in question, find the general solution:

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

⇒ sec^{2}xdx = dt

Thus, the equation (1) becomes,

⇒ te^{tanx} = (t – 1)e^{t} + C

⇒ te^{tanx} = (tanx – 1)e^{tanx} + 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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