What is the general solution of the differential equation ? # dy/dx=y+c#

Question

1383 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-21T02:57:38

# y = Be^x - c #

We have:

# dy/dx = y + c#

This is a First Order Linear Differential Equation which we can rewrite as a separable equation and thus "separate the variables" to get:

# 1/(y + c) \ dy/dx = 1 #

# :. int \ 1/(y + c) \ dy = int \ dx #

Which consists of standard integral function ; so we can integrate to get

# ln|y + c| = x + A #

Taking exponentials we get:

# |y + c| = e^(x + A) #

And as the exponential is positive for all values; we must have:

# y + c = e^xe^A #

Which we can write as:

# y = Be^x - c #