Consider the differential equation:

The initial condition is y(0) = 1. Construct the Maclaurin series for y(x).

I know I'm supposed to differentiate it, but I don't remember how to use the initial condition to start me off...

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- Feb 11th 2010, 07:58 AMBlackBlazeMaclaurin Series for a Differential Equation
Consider the differential equation:

The initial condition is y(0) = 1. Construct the Maclaurin series for y(x).

I know I'm supposed to differentiate it, but I don't remember how to use the initial condition to start me off... - Feb 11th 2010, 08:21 AMchisigma
The McLaurin series for y is...

(1)

... so that...

(2)

The 'initial condition' extablishes that . If now write the DE in terms of (1) and (2) we obtain...

(3)

.. so that is...

(4)

Kind regards - Feb 11th 2010, 08:44 AMCalculus26
see attachment