anonymous 4 years ago find a polynomial f(x) that satisfies the equation xf''(x) + f(x) = x^2

1. anonymous

do you know about diffrential equation?

2. anonymous

which equation?

3. anonymous

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

4. shubhamsrg

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5. anonymous

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

6. anonymous

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

7. anonymous

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