1.

Solve the differential equation dy/dx + y sec x = tan x, 0 ≤ x < π/2.

Answer»

P = secx Q = tan x 

IF = e∫sec xdx = elog(sec x + tan x) = secx + tanx 

y x IF = ∫Q x IF 

y (sec + tan x) = ∫(sec x + tan x) tan x.dx 

= ∫sec x.tan x + ∫ tan2 x.dx 

= secx + ∫(sec2 x - 1) dx 

y(sec x + tan x) = sec x + tan x - x + c



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