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| #