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



This Question is Closed

uzumakhi
Best Response
You've already chosen the best response.
0
do you know about diffrential equation?

heydayana
Best Response
You've already chosen the best response.
0
which equation?

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

shubhamsrg
Best Response
You've already chosen the best response.
0
*

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

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

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