Explain why or why not Determine whether the following statements are true and give an explanation or counter example.
a. The differential equation y′ + 2y = t is first-order, linear, and separable.
b. The differential equation y′y = 2t 2 is first-order, linear, and separable.
c. The function y = t + 1 /t satisfies the initial value problem ty' + y = 2t, y(1) = 2.
d. The direction field for the differential equation y′(t)= t + y(t) is plotted in the ty-plane.
e. Euler’s method gives the exact solution to the initial value problem y′ = ty2, y(0) = 3 on the interval [0, a] provided a is not too large.