let y=f(x) be the particular solution for the differential equation with the initial condition y(-1_=3/2
To find the particular solution y = f(x) for a differential equation with an initial condition, we need to integrate the differential equation and solve for any unknown constants using the given initial condition.
Since you haven't mentioned the differential equation, I won't be able to provide the specific steps for solving it and finding the particular solution. However, I can guide you through the general steps.
1. Write down the given differential equation. It will likely involve y, x, and possibly derivatives of y.
For example, it could be in the form dy/dx = f(x, y).
2. Integrate both sides of the differential equation with respect to x, treating y as the variable of integration.
This will help eliminate the derivative and solve for y in terms of x and any constants.
3. If the equation has any unknown constants, substitute the initial condition (y(-1) = 3/2) into the equation.
This will allow you to solve for the constants and obtain a specific solution.
4. Once you have determined the values of the constants, your particular solution y = f(x) will be determined.
Remember, the steps may vary depending on the specific differential equation. If you provide the equation, I can assist you further in finding the particular solution.