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7. [4 points] Consider the differential equation = f(y). A young numerical analyst proposes new numerical scheme giving rise to the following finite difference approximation: y_{n+1}=y_{n}+\frac{1}{4} h f\left(y_{n+1}\right)+\frac{3}{4} h f\left(y_{n}\right) where y, and Yn+1 represent solutions at times t, and t+1, respectively, and h = tn+1- tn is-the step size. Let f(y) = -iy with (i = v-1); identify, with proper mathematical reasoning-and analysis, whether or not h = 1 will provide a stable solution. Show all steps. Box youranswer.

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