Taylor Series Solutions of Differential Equations
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Hi there, I have a question regarding Taylor Series ODE which can be located here http://nullspace8.blogspot.com/2011/10/14.html. can someone please take a look? Full working step by step solution in pdf or word please. If you think the bid is insufficient and you can do it, please respond with a counter bid. Thank you.
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Solution Summary
We compute the Taylor series up to given limits of the solutions to various first-order differential equations with given initial values.
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a) We have y' = x^2 y^2 with initial condition y(0) = 1 and we wish to compute the Taylor series of y(x) up to n=2. First we write
y = c_0 + c_1 x + c_2 x^2 + O(x^3).
Since y(0) = 1 we have c_0 = 1. Now
y' = c_1 + 2 c_2 x + O(x^2).
But this is also equal to
x^2 y^2
= x^2(c_0 + c_1 x + c_2 x^2 + O(x^3)
= c_0 x^2 + c_1 x^3 + c_2 x^4 + O(x^5).
Equating terms multiplying 1 and x, ...
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