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Advanced MathQ&A LibraryA point is an ordinary point of a non-homogeneous linear second order differential equation, y"+p(x)y'+q(x)y=f(x)is p, q, f are analytic at x0. Moreover, our theorem on the existence of power series solutions extends to such differential equations, ie, we can find power series solutions of non-homogeneous linear differential equations in the same manner as we have for homogeneous equations...almost. Find the series solution to the non-homogeneous initial value problem. Note: BEWARE THE THEOREM OF EQUIVALENT SERIES!!!Find the first five nonzero terms of the series solution to:y"+2y'+y=ex, y(0)=2, y'(0)=1Question

Asked Jul 8, 2019

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A point is an ordinary point of a non-homogeneous linear second order differential equation,

y"+p(x)y'+q(x)y=f(x)

is p, q, f are analytic at x_{0}. Moreover, our theorem on the existence of power series solutions extends to such differential equations, ie, we can find power series solutions of non-homogeneous linear differential equations in the same manner as we have for homogeneous equations...almost. Find the series solution to the non-homogeneous initial value problem. Note: BEWARE THE THEOREM OF EQUIVALENT SERIES!!!

Find the first five nonzero terms of the series solution to:

y"+2y'+y=e^{x}, y(0)=2, y'(0)=1

Step 1

Consider the differential equation:

Step 2

Let a power series solution of the differential equation be

Step 3

Substitute *y*, *y’ *and *y’’* in t...

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