Regular Power Series Solution

Solution of

y''+cos(x) y=0

for y(x) with y(0)=1 and y'(0)=0.

An exact solution can be found in this case, and can

be compared with the series solution.

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Let's find a solution valid out to . The first step in finding a series solution is to find an expansion for Cos[x]:

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Here are the unknowns in the expansion of *y**(**x**)* that we must solve for:

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Here are the algebraic equations for those coefficients:

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We actually don't need the TableForm for the math, it is just nice to look at:

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a[0]+2 a[2]==0 |

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So here is the series solution that satisfies the specified initial conditions:

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Now find exact solution:

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Plot approximate (red) and exact (green) solutions:

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