Question

Solve numerically the IVP

d²y/dt² + 7y × dy/dt + y = 7 sint, with y(0) = 0.5, dy/dt(0) = -0.5
in the interval 0 ≤ t ≤ 55. Include the M-file in your report.
Is the behavior of the solution significantly different from that of the solution of (7)?

Answer 1

To solve the initial value problem numerically, you would need to define the system of differential equations and use numerical methods like Euler's method or the Runge-Kutta method. I will provide you with the M-file code for solving this.

Step-by-step explanation:

To solve the IVP numerically,

First, we need to define the system of differential equations. Letting z = dy/dt, we have:

d/dt(y) = z

d/dt(z) = -7z - y + 7sin(t)

With the initial conditions y(0) = 0.5 and z(0) = -0.5.

We can solve this system of differential equations using numerical methods like Euler's method or the Runge-Kutta method. I will write the M-file code for you to solve this numerically.