What is the general solution of the differential equation ? $\frac{d y}{d x} = y + c$ $dy/dx=y+c$

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Answer 1 · 2017-11-21T02:57:38

$y = B e^{x} - c$ $y = Be^x - c$

We have:

$\frac{d y}{d x} = y + c$ $dy/dx = y + c$

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:

$y = Be^x - c$

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