The general solution of the differential equation can be derived by observing the equation provided. The expression ‘y 4y 0’ seems to be a typographical error. A more standard form might be ‘y’ = 4y’ or possibly describing a higher order ordinary differential equation.
Assuming you are referring to the first-order linear differential equation y’ = 4y, it can be solved using the method of separation of variables.
To solve it, we can rearrange the equation:
dy/y = 4 dx
Next, we integrate both sides:
∫(1/y) dy = ∫4 dx
This gives:
ln|y| = 4x + C
Where C is the constant of integration. Exponentiating both sides leads us to:
y = e^(4x + C) = e^C * e^(4x)
We can denote K = e^C, which is a constant and thus the general solution can be written as:
y = Ke^(4x)
This solution represents an exponential function which scales with respect to the variable x, where K is determined by initial or boundary conditions as needed.