Determine the recursive formulas for the Taylor method of order 2 for the initial value problem .
Apply the chain rule.
So, the equation is
The recursive formula is
for order p = 2 then
Where starting points are .
Hence the solution is role="math" localid="1664314543589"
If the resistance in the RL circuit of Figure 3.13(a) is zero, show that the current I (t) is directly proportional to the integral of the applied voltage E(t). Similarly, show that if the resistance in the RC circuit of Figure 3.13(b) is zero, the current is directly proportional to the derivative of the applied voltage.
In Problems 23–27, assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes for one-half of the substance to disintegrate. If initially there are 300 g of a radioactive substance and after 5 yr there are 200 g remaining, how much time must elapse before only 10 g remain?
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