Question

(Part 1) Find all of the solutions of the given differential equations:

a.) y' = -2^y (answer should be y = -(1 / ln2) * ln(t * ln(2) + c))

(Part 2) Find the solution of the IVP:

b.) y' = -2y³, y(0) = 0

c.) y' = 1 + cos(y), y(0) = pi / 2 (answer should be y(t) = 2arctan(1 + t))

d.) y' = sqrt(1 - y²), y(0) = 0 (Hint: y' > 0)

Please show work!

Answer 1

the differential equations have been solved by basic integration method

and also using the intial conditions the values have been written