The highest derivative terms present in DE is of 2nd order.

Eigen value of a Skew-symmetric matrix are either zero or pure imaginary in conjugate pairs.

For a function x(t) trigonometric fourier series is

For an even function x(t),B^{n} = 0

Since given function is even function so coefficient B^{n} = 0, only cosine and constant

terms are present in its fourier series representation.

Constant term :

Constant term is negative.

Given differential equation

No Explaination.

Consider differential equation with the initial condition y(0) = 0. Using Euler’s first order method with a step size of 0.1, the value of y(0.3) is

Taking step size h = 0.1, y(0) = 0

From table, at x = 0.3,y(x = 0.3) = 0.031

By final value theorem