Question

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

Answer 1

do you know about diffrential equation?

Answer 2

which equation?

Answer 3

undetermined coefficients: try Ax^2 +Bx +c = yp

Answer 4

*

Answer 5

firstly we divide by x and then integrating both sides twice will i guess give the answer

Answer 6

by dividing with x we get
\[f''(x) + \frac{ f(x) }{ x } = x\]

Answer 7

we write it as
\[f''(x) = x - \frac{ f(x) }{ x }\]
now integrate both sides