Solve the given differential equation by separation of variables, dy/dx = e5x + 4y.
We will be solving this by using the first-order separable ordinary differential equation.
Answer: The general solution of differential equation dy/dx = e5x + 4y is y = -1/4 ln(-4/5 e5x - 4C).
Let's solve this step by step.
Given, differential equation: dy/dx = e5x + 4y
y' = e5x + 4y
A first-order ordinary differential equation has the form of N(y). y' = M(x)
Rewrite the equation:
1/e4y y' = e5x
1/e4y dy = e5x dx
Integrate on both sides, we get:
-1/4 e-4y = 1/5 e5x + C
e-4y = -4/5 e5x - 4C
Apply ln on both sides:
ln(e-4y) = ln(-4/5 e5x - 4C)
-4y = ln(-4/5 e5x - 4C)
y = -1/4 ln(-4/5 e5x - 4C)