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**The Questions**

Let y(x) be the position of a particle at time x. Suppose that we know that

the velocity of a particle satisfies the differential equation:

y'(t) = ty

with y(0) = 1. We will try to give a reasonable method to approximate some of

the positions of the particle.

a.) Integral both sides to show that:

y(x) = integral(x to 0) ty(t) dt +1

b.)In your own words, explain how a numerical technique could be set up to

approximate solutions to the differential equation;

y'' = ty

Hint: integration by parts.

**3. My attempt at a solution**

a.) Since y'(t) = ty, when we integrate both sides --> y(t) = (t/2)y^2. I don't see how this can turn to a y(x)...