Solve the given differential equation by separation of varia

Solve the given differential equation by separation of variables.

dy/dx = e^{4x + 5y}

Solution

dy/dx = e^(4x+5y)

=>

dy/e^5y = e^4xdx

=>

e^-5y dy = e^4xdx

=>
e^(-5y)/-5 = e^(4x)/4 +c

=>

4/e^(5y) + 5e^(4x) = C

=>

5e^(4x+5y) +4 = Ce^(5y)