find the particular solution y=f(x) to the differential equation with the initial condition y(-1)=3/2

To find the particular solution y = f(x) to a differential equation, we need to know the general form of the differential equation itself. Without that information, we won't be able to provide a specific solution.

However, I can guide you through the general process of finding a particular solution to a differential equation with an initial condition.

1. Start by writing down the given differential equation. The differential equation will include the derivative of y with respect to x, and possibly other terms involving y and x.

2. Solve the differential equation symbolically to obtain a general solution. This general solution will typically involve a constant of integration, represented by "C".

3. Apply the initial condition to find the particular value of the constant of integration. In this case, since the initial condition is y(-1) = 3/2, substitute this value for x and y into the general solution.

4. Solve for the constant of integration using the initial condition. Simplify the equation and solve for C.

5. Once you have the value of the constant of integration, substitute it back into the general solution to get the particular solution of the differential equation. This particular solution will have the form y = f(x).

By following these steps, you can find the particular solution for a given differential equation with an initial condition.