need help also this dy / dx = sec2y / 1 + x2 xdv / dx = 1 - 4v2 / 3v dx / dt - x

Question

need help

also this

dy / dx = sec2y / 1 + x2 xdv / dx = 1 - 4v2 / 3v dx / dt - x3 = x dy / dx = 3x2(1 + y2)3/2 y-1 dy + yecos x sin x dx = 0 (x + xy2)dx + ex2y dy = 0 y? = x3(1 - y), y(0) = 3 dy/dx = (1 + y2)tan x, y(0) = root3 1 / 2 dy / dx = rooty + 1 cos x, y(pi) = 0 x2dy / dx = 4x2 - x - 2 / (x + 1)(y + 1), y(1) = 1 1 / theta dy / dtheta = y sintheta / y2 + 1 , y(pi) = 1 x2 dx + 2y dy = 0, y(0) = 2 t-1dy / dt = 2cos2y, y(0) = pi / 4 dy / dx = 8x3e-2y, y(1) = 0 dy /dx = x2(1 + y), y(0) = 3 rootydx + (1 + x)dy = 0, y(0) = 1

Explanation / Answer

dy/sec^2y = dx/(1+x^2)

cos^2y dy=dx/(1+x^2)

(1+ cos2y)dy/2 =dx/(1+x^2)

integrate

y/2 +(sin2y)/4= tan^-1 x +c

y+0.5(sin2y)=2tan^-1 x +C

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