Question

y(t) is the solution of the differential equation dy/dt​ =0.7/(t+y)² When t=0,y=0.8 Use the midpoint method with a time step of h=0.08, calculate y(h)

Answer 1

To find y(h) when t=0 and y=0.8 for the differential equation dy/dt = 0.7/(t+y)^2, you can use the midpoint method with a time step of h=0.08.

Step-by-step explanation:

To solve the differential equation, we can use the midpoint method with a time step of h=0.08. Given that dy/dt = 0.7/(t+y)^2, we need to find y(h) when t=0 and y=0.8. Here are the steps:

1. Start with t=0 and y=0.8.
2. Calculate the increment k1 by evaluating the equation at t=0 and y=0.8.
3. Calculate the midpoint values for t and y by adding half of h to t and y, respectively.
4. Calculate the increment k2 by evaluating the equation at the midpoint values for t and y.
5. Use the formula y(h) = y + h*k2 to calculate the value of y at h.
6. Substitute the values into the formulation and calculate the value of y(h).

Using these steps, you can calculate the value of y(h) with the given differential equation.