y' = ty, y(0) = 1?
(a) Use Euler's method to approximate the solution of the IVP at t = 1 with step sizes 1, 1/2, 1/4, and 1/8.
with step size 1: y(1) = ?
with step size 1/2: y(1) = ?
with step size 1/4: y(1) = ?
with step size 1/8: y(1) = ?
(b) Solve the IVP exactly and compute the value of y(1).
y(t) = ?
y(1) = ?
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(b) This is a variables separable differential equation. You rearrange it from dy/dt = ty into (1/y)*dy = t*dt and then integrate each side on its own. Don't forget to introduce a constant of integration although you only need to do this on one side.