Finding a Particular Solution for a Non-Homogeneous Differential Equation

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10. Consider the equation *) y'' + y = exp(-x^2)sec(x). Solutions of the corresponding homogeneous equation are of course cos(x) and sin(x).
We want a particular solution yp of *).
a) Try to use undetermined coefficients to find yp.
b) Try to do it using variation of parameters.
c) Both methods fail. Explain why.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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