Hi everybody, I have absolutely no idea how to tackle this problem: Let p(x) be a solution of the differential equation with initial conditions and . Find and . Any help would be greatly appreciated. Thank you!
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Originally Posted by gundu24 Hi everybody, I have absolutely no idea how to tackle this problem: Let p(x) be a solution of the differential equation with initial conditions and . Find and . Any help would be greatly appreciated. Thank you! Did you try anything on this? Since p(x) satisfies the equation, . You know the values of x, y, and y' at -1 so you can directly calculate the right side. To find p'"(-1), Differentiate both sides of the equation above and evaluate at x=-1.
The problem is quite interesting because, applying the procedure described by HalsofIvy, You can iteratively compute the quantities and that allows You to obtain the Taylor expansion of around ... (1) Kind regards
Yes, that's a standard, though very slow and not very practical, method of finding power series solutions to differential equations.
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