If someone can help me with this ODE I would greatly appreciate it. Thank you in advance!

Question

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Consider the differential equation

dx/dt = 1/2x

This is a separable O.D.E., so we know how to find all of its solutions: they are of the form

x(t) = sqrt(t+c)

where C is a constant. Imposing the initial condition x(1) = 1 fixes C = 0. Then we have x(2)= sqrt(2)

Use Euler's method with h = 1/2 to find an approximation to sqrt(2).

Provide a numeric answer rounded to two decimal places.

Answer 1

1/4