Question

Find the first four non-zero terms in the power series representation about the ordinary point x0 = 0 of the solution of the initial value problem: y" + 4eˣy + xy = 0; y(0) = 2; y(0) = 3

Answer 1

To find the first four non-zero terms in the power series representation about x0 = 0, we need to write the differential equation in standard form and assume the solution can be represented as a power series. Substituting this power series into the differential equation and equating like powers of x, we can solve for the coefficients.

Step-by-step explanation:

To find the first four non-zero terms in the power series representation about x0 = 0, we first need to write the differential equation in standard form:

y'' + 4e^xy + xy = 0

Next, we can assume that the solution can be represented as a power series:

y(x) = a0 + a1x + a2x^2 + a3x^3 + ...

Substituting this power series into the differential equation and equating like powers of x, we can solve for the coefficients a0, a1, a2, and a3.