Question

Y(t) is the solution of the differential equation dy/dt = 0.9/(t+y)² When t=0,y=0.9 Use the midpoint method with a time step of h=0.1,

calculate y(h)= Please correct your answers to three decimal places.

Answer 1

To solve the differential equation using the midpoint method, we find y(h) by following the steps of the method.

Step-by-step explanation:

To solve this differential equation using the midpoint method, we first need to find the value of y(h). We start with the initial condition given: t=0 and y=0.9.

Using the midpoint method, we have the following steps:

1. Calculate the midpoint:

k1 = 0.9/(0+0.9)2 = 1.111

k2 = 0.9/(0.1+0.9+0.555)2 = 0.204

2. Update the value of y(h):

y(h) = y(0) + h * k2 = 0.9 + 0.1 * 0.204 = 0.921

Therefore, y(h) = 0.921, correct to three decimal places.