Find the General Solution of the Given Second Order Differential Equation 2y y’

To solve the differential equation of the form 2y y’ = 0, we can start by breaking it down into its factors. Here, the equation can be rewritten as:

2y = 0  or  y' = 0

1. **Solving the first factor:**

From 2y = 0, we can conclude that:

y = 0

This gives us one particular solution where the function is constantly zero.

2. **Solving the second factor:**

Now for y’ = 0, it indicates that the derivative of y with respect to the independent variable (often x or t) is zero. This means that y must be a constant value. Thus:

y = C

where C is any constant.

3. **General Solution:**

Combining both solutions, we can express the general solution of the differential equation as:

y = 0  or  y = C

In summary, the general solution to the differential equation 2y y’ = 0 includes the trivial solution (where y is always zero) and the solutions where y takes any constant value.