Question

Solve the Initial Value Problem x² y ′′ −xy ′ +y=x³ ;y(1)=0,y ′ (1)=1

Answer 1

To solve the given initial value problem, we can use the method of power series.

Step-by-step explanation:

To solve the given initial value problem, we can use the method of power series. Let's assume that the solution can be expressed as a power series: y(x) = Σ a_n (x - 1)^n. We can then substitute this series into the differential equation and solve for the coefficients a_n. Using this approach, we can obtain the solution to the initial value problem.