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# Solving an Initial value problem by using Taylor's method

Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual values of y.

See attached file for full problem description.

(5.3)
6. Given the initial-value problem

, ,
with exact solution :
a. Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual values of .
b. Use the answers generated in part (a) and linear interpolation to approximate the following values of , and compare them to the actual values.
i.

#### Solution Preview

Please see the attached file.

(5.3)
6. Given the initial-value problem

, ,
with exact solution :
a. Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual values of .

Let y' be d1 and it is given as;

for higher order taylor method we need second derivative of y. since y is a function of t we need to use chain rule to find y". Lets call y" as d2;

y"=d2

Note that we have y' already
...

#### Solution Summary

The expert solves an initial value problem by using Taylor's methods. Linear interpolation generated are examined.

\$2.19