# Solve the given differential equation by separation of variables. dy/dx = e^{(5x+4y)}.

**Solution:**

Given: Differential equation is dy/dx = e^{(5x+4y)}.

dy/dx = e^{(5x+4y)}. {a^{m + n }= a^{m }× a^{n}}

dy/dx = e^{5x} × e^{4y}

Separating the variables (a and its differential in one side and y and its differential in another side )

⇒e^{-4y}dy = e^{5x}dx

Integrating on both the sides

⇒ \(\int e^{-4y}dy = \int e^{5x} dx\)

But \(\int e^{ax}dx\) = (e^{ax}/a) + c

⇒ \(\int e^{-4y}dx\) = (e^{-4y}/-4) + c and \(\int e^{5x}dx\) = (e^{5x}/5) + c

Therefore, (e^{-4y}/-4) = (e^{5x}/5) + c

Where c is constant of integration.

## Solve the given differential equation by separation of variables. dy/dx = e^{(5x+4y)}.

**Summary:**

The general solution of the differential equation by separation of variables. dy/dx = e^{(5x+4y)} is (-e^{-4y}/4) = (e^{5x}/5) + c.