Differential Equations and Their Applications assignment. only 6 questions.

Question 1 (3 points) Rewrite the following equation with the variables separated. y' tan(y) = sin(y) (2x+1)Question 2 (3 points) Rewrite the following equation with the variables separated. y' = 6x342 + 2m + 65:2 + 2y I Question 3 (3 points) Rewrite the following equation with the variables separated. y' + 6x sin(y) = 5 sin(y) Question 4 (3 points) Find the general solution to: 2vy dx dy - - ex = 0, for y > 0uestion 5 (3 points) Given the initial condition y(0) = 2, find the particular solution of the equation ely' - 2x = 0Question 6 (3 points) Find the equation of the curve that passes through the point (1, 3) and has a slope of V at any point (x, y]. (where y > O and x > 1] x+1