Question

Solve the differential equation 2xy''–y' = 0 by power series method.​

Answer 1

Step-by-step explanation:

Explanation:

Assuming a power series solution like this:

y=a0+a1x+a2x2+a3x3+...=∞∑0anxn

⇒y′=∞∑1nanxn−1        y''=∞∑2n(n−1)anxn−2

With this power series:

y''+2xy'+y=0

⇒∞∑2n(n−1)anxn−2=∑∞0(m+2)(m+1)am+2xm+2x∞∑1nanxn−1+∞∑