Solve: dy/dx - ytanx = sinx?

Answer 1

y' - y(sin x / cosx) = sin x
<=> y' cos x - y sin x = sin x cos x
<=> d/dx (y cos x) = sin x cos x
<=> y cos x = ∫sin x cos x dx
= ∫ u du where u = sin x, du = cos x dx
= 1/2 sin^2 x + c
So y = (1/2 sin^2 x + c) / cos x
= 1/2 sin x tan x + c sec x

Answer 2

discover the final answer with the aid of placing apart the variables then integrating: dy / dx = (y + 2)sinx dy / (y + 2) = sinx dx ? a million / (y + 2) dy = ? sinx dx ln|y + 2| = -cosx + C ln|y + 2| = C - cosx y + 2 = ?^(C - cosx) y + 2 = ?? / ?^(cosx) y + 2 = C / ?^(cosx) y = C / ?^(cosx) - 2 discover the particular answer with the aid of fixing for the consistent: whilst x = ? / 2, y = 4 C - 2 = 4 C = 6 y = 6 / ?^(cosx) - 2

Answer 3

Im assuming you want to solve for the equation in terms of "x"... well, to do this, start by getting all of your y's and your x's on different sides, integrate and simplify! That will help :)