# Frobenius - These approximations are graphed below Note...

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MATH 342 – 010 Differential Equations with Linear Algebra, October 28, 2009 Series solutions Consider the equation y - y =0 The solution y 1 with y 1 (0) = 1, y 1 (0) = 0 is cosh x The first three approximations to the series are given by y 1 1 (1.1) y 1 1 + x 2 /2 (1.2) y 1 1 + x 2 /2 + x 4 /24 (1.3)

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Unformatted text preview: These approximations are graphed below. Note that with each increasing term, the range of x for which the polynomial is a good approximation widens. In increasing order of thickness: Polynomial Approximations (1.1), (1.2) and (1.3) and cosh x vs x for x ε [-3, 3]...
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Frobenius - These approximations are graphed below Note...

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