What is the general equation of dy/dx =e^(x+y)?
2 Answers
Apr 5, 2018
Explanation:
This is a separable differential equation so
Apr 5, 2018
y = -ln|C-e^x|
Explanation:
We have:
dy/dx = e^(x+y)
Which we can write as
dy/dx = e^(x) e^(y)
We can collect terms for similar variables:
e^(-y) dy/dx = e^x
Which is a separable First Order Ordinary non-linear Differential Equation, so we can "separate the variables" to get:
int \ e^(-y) \ dy = int e^x \ dx
Both integrals are those of standard functions, so we can use that knowledge to directly integrate:
-e^(-y) = e^x - C
And we can readily rearrange for
e^(-y) = C-e^x
:. -y = ln|C-e^x|
Leading to the General Solution:
y = -ln|C-e^x|