Consider the IVP y = x + 2y, y(0) = 1 A) (8 pts) Use Euler's method to obtain an approximation of y(0.5) usingh = 0.25 for the given IVP (Use four-decimal approximation) B) (12 pts) Use Euler's method to obtain an approximation of y(0.5) usingh = 0.1 for the given IVP (Use four-decimal approximation) A bacteria culture initially has 100 number of bacteria and doubles in size in 2hours. Assume that the rate of increase of the culture is proportional to the size. Write the initial value problem for the bacteria culture and solve it ts) How long will it take for the size to triple? Verify that y(x) = c1 cos(6x) + c2 sin(6x) is a solution of y" + 36y = 0 s) Either solve the boundary value problem y^{\prime \prime}+36 y=0, y(0)=0, y\left(\frac{2 \pi}{6}\right)=1 or else show that it has no solution