If `dy/dx+3/cos^2xy=1/cos^2x,x in((-pi)/3,pi/3)and y(pi/4)=4/3," then "y(-pi/4)` equals

If (dy)/(dx)+3/(cos^(2)x)y=1/(cos^(2)x),xin((-pi)/3,(pi)/3), and y((pi)/4)=4/3 , then y(-(pi)/4) equals 1/3+e^(k) . The value of k is __________.

If (dy)/(dx)+3/(cos^(2)x)y=1/(cos^(2)x),xin((-pi)/3,(pi)/3), and y((pi)/4)=4/3 , then y(-(pi)/4) equals 1/3+e^(k) . The value of k is __________.

If (dy)/(dx) + (4)/(cos^2 x) y = (1)/(cos^2 x) , x in ((-pi)/(3) , pi/3) " and " y (pi/6) = 4/3 " then " y (- pi/6) equals ,

Let y(x) be the solution of the differential equation (dy)/(dx)+(3y)/(cos^2x)=1/(cos^2x) and y(pi/4)=4/3 then vaue of y(-pi/4) is equal to (a) -4/3 (b) 1/3 (c) e^6+1/3 (d) 3

Let y(x) be the solution of the differential equation (dy)/(dx)+(3y)/(cos^(2)x)=(1)/(cos^(2)x) and y((pi)/(4))=(4)/(3) then vaue of y(-(pi)/(4)) is equal to (a)-(4)/(3)(b)(1)/(3)( c) e^(6)+(1)/(3)(d)3

Let y=y(x) be the solution of the differential equation, dy/dx+y tan x=2x+x^(2)tanx, x in(-pi/2,pi/2), such that y(0)= 1. Then (a) y'(pi/4)-y'(-pi/4)=pi-sqrt 2 (b) y'(pi/4)+y'(-pi/4)=-sqrt 2 (c) y(pi/4)+y(-pi/4)=-pi^(2)/2+2. (d) y(pi/4)-y(-pi/4)=sqrt 2

If x=y cos((2 pi)/(3))=z cos((4 pi)/(3)), then xy+yz+zx=

If y=(sin x - cos x)^((sinx-cosx)),(pi)/(4)ltxlt(3pi)/(4) , then find (dy)/(dx) .

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to -(1)/(3)(2)(4)/(3) (3) (1)/(3)(4)-(2)/(3)