How do you find the general solution to dy/dx+e^(x+y)=0?

1 Answer
Jul 24, 2016

y = ln ( 1/(e^x + C) )

Explanation:

dy/dx+e^(x+y)=0

this is separable

dy/dx= - e^(x+y)

dy/dx= - e^x e^y

e^(-y) dy/dx= - e^x

int\ e^(-y) dy/dx \ dx=int - e^x \ dx

int\ e^(-y) \ dy=- int e^x \ dx

-e^(-y) =- e^x + C

e^(-y) = e^x + C

e^(y) = 1/(e^x + C)

y = ln ( 1/(e^x + C) )