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

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uzumakhiBest ResponseYou've already chosen the best response.0
do you know about diffrential equation?
 one year ago

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

nitzBest ResponseYou've already chosen the best response.0
firstly we divide by x and then integrating both sides twice will i guess give the answer
 one year ago

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

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