How do you find the explicit formula for a power series?
Find Explicit Formula for Power Series
- I took derivative of the power series and got. (−1)n∑∞n=0(xn) The explicit formula would be (−1)n 11−x.
- I integrated the power series back to the original form and integrated the explicit formula as well. The explicit formula I got was −(−1)n ln(|1-x|) I believe this is incorrect.
What is a series solution?
In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
How to solve differential equations?
Put the differential equation in the correct initial form,(1).
What is a linear first order differential equation?
A first order ordinary differential equation is linear if it can be written in the form. y′ + p(t) y = g(t) where p and g are arbitrary functions of t. This is called the standard or canonical form of the first order linear equation. We’ll start by attempting to solve a couple of very simple equations of such type.
What is the second order differential equation?
Second-Order Linear Equations. The order of a differential equation is the order of the highest derivative appearing in the equation. Thus, a second‐order differential equation is one that involves the second derivative of the unknown function but no higher derivatives.