I have this simple differential equation: y ′ = ( tan ⁡ x ) y...

pablos28spainzd

pablos28spainzd

Answered

2022-07-01

I have this simple differential equation: y = ( tan x ) y .
after integrating y y ( x ) = tan x
i came up with log y ( x ) = log cos ( x ) + 1.
now my question is this one: why e log cos ( x ) = sec ( x ) ?

Answer & Explanation

Jamarcus Shields

Jamarcus Shields

Expert

2022-07-02Added 17 answers

I suppose that log ( x ) is for ln ( x )
e log cos ( x ) = ( e log cos ( x ) ) 1 = ( cos ( x ) ) 1 = 1 cos ( x ) = sec ( x )

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