(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the following equation by a power series and also by separation of variables. Check that the two agree.

2. Relevant equations

N/A

3. The attempt at a solution

Power Series:

[tex] (1+x) \frac{dy}{dx} = y [/tex]

[tex] (1+x) \frac{1}{dx} = y \frac{1}{dy} [/tex]

The power series is:

[tex] (1+x) \equiv 1+x+0x^2+0x^x [/tex] ...

Thus

[tex] \frac{1 + x}{dx} = \frac{y}{dy} [/tex]

Separation by Variables:

[tex] (1+x) y' = y [/tex]

[tex] y' = \frac{1}{((1+x)} y [/tex]

[tex] x'=g(t)h(x) [/tex]

[tex] H(x) = G(t) + C [/tex]

[tex] H=\int \frac{dx}{h(x)} ; G=\int g(t)dt [/tex]

[tex] H=\int \frac{dy}{y} \equiv \int \frac{1}{y} dy = ln y [/tex]

[tex] G = \int \frac{1}{1+x} dx = ln(1 + x) [/tex]

[tex] ln y = ln (1+x) + c [/tex]

[tex] y = 1 + x + c [/tex]

These two methods haven't agreed for this question. i think the problem lays in my Power Series.

Anyone got any idesa?

TFM

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# Homework Help: Solving an ODE: The Pwer Series and Seperation of Variables

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