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heydayana
 2 years ago
find a polynomial f(x) that satisfies the equation xf''(x) + f(x) = x^2
heydayana
 2 years ago
find a polynomial f(x) that satisfies the equation xf''(x) + f(x) = x^2

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uzumakhi
 2 years ago
Best ResponseYou've already chosen the best response.0do you know about diffrential equation?

Algebraic!
 2 years ago
Best ResponseYou've already chosen the best response.1undetermined coefficients: try Ax^2 +Bx +c = yp

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0firstly we divide by x and then integrating both sides twice will i guess give the answer

uzumakhi
 2 years ago
Best ResponseYou've already chosen the best response.0by dividing with x we get \[f''(x) + \frac{ f(x) }{ x } = x\]

uzumakhi
 2 years ago
Best ResponseYou've already chosen the best response.0we write it as \[f''(x) = x  \frac{ f(x) }{ x }\] now integrate both sides
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