If y = y x is the solution of the differential equation d y d x + tan x y = sin x , 0 ≤ x ≤ π 3 , with y 0 = 0 , then y π 4 is equal to

Question

If y = y x is the solution of the differential equation d y d x + tan x y = sin x , 0 &#8804; x &#8804; &#960; 3 , with y 0 = 0 , then y &#960; 4 is equal to

Aicharya · Accepted Answer

d y d x + tan x y = sin x ; &#160; 0 &#8804; x &#8804; &#960; 3 I . F . = e &#8747; tan x d x = e ln sec x = sec x y sec x = &#8747; tan x d x + C y sec x = ln sec x + C x = 0 , &#160; y = 0 &#160;&#160; &#8658; &#160; C = 0 y sec x = ln sec x y = cos x &#183; ln sec x y x = &#960; 4 = 1 2 &#183; ln 2 y x = &#960; 4 = 1 2 2 log e 2

If y = y x is the solution of the differential equation d y d x + tan x y = sin x , 0 ≤ x ≤…

Solution

If y = y x is the solution of the differential equation d y d x + tan x y = sin x , 0 &#8804; x &#8804;…

Solution

If y = y x is the solution of the differential equation d y d x + tan x y = sin x , 0 ≤ x ≤…