Rewrite the equation with the variables separated. 2y' = 3xty O dy 2-3y = 3: dx 0 3'dy = 32 2 dx O dy 34 2 dx O dy 34 = 2 .3 dxRewrite the equation with the variables separated. dV dt = 6tvV O AP U = 612 dt O dv dt 6t O dV = 6tdt O VVdV = 6tdtRewrite the equation with the variables separated. dy + I O vydy = (ex + 1) dx dy O /y-1 = ex dx O dy y = (ex - 1) da dy O = (ex +1) da\fGiven the initial condition y(0) = 3, what is the particular solution of the equation ex-29 = y'? In(2ex -403.429) O y= 2 In(2ex +401.429) o y= 2 In(2ex -401.429) O y= 2 In(2ex + 403.429) O y= 2What is the equation of the curve that passes through the point (1, 3) and has a slope of get any point (1:, y), where y > 0? if the acceleration A(t) of an object is proportional to the square root of its speed S[t). what is the differential equation for the acceleration of the object? Do not solve. o A(t)='fdf=k\\/S o =kv71 O =kvl The rate of change of R is inversely proportional to R(x) where R > 0. If R(0) = 25, and R(2) = 10, find x, such that R(x) = 16. O -3 O -2.893 O 1.406 0 4