Question

Solve y = ptanp+log(cosp)
Where p =dy/dx

Answer 1

Given : y = ptanp + log(cosp) where p = dy/dx

To find : x in terms of p

Solution:

y = ptanp + log(cosp)

p = dy/dx

differentiating wrt x

=> dy/dx  = p sec²p (dp/dx)  + tanp (dp/dx)  +  (1/Cosp)(-Sinp)(dp/dx)

=> dy/dx  = p sec²p (dp/dx)  + tanp (dp/dx)  - tanp(dp/dx)

=> dy/dx  = p sec²p (dp/dx)

dy/dx = p

=> p = p sec²p (dp/dx)

=> 1 = sec²p (dp/dx)

=> dx = sec²p (dp)

integrating both sides

=> x  = tanp + c

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