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

The general solution of dy/dx=ex+y is equal to ex+ e-y= C, and the solution of dy/dx=ex-y is given by ex – ey= C. Here C denotes an arbitrary constant. Let us learn to solve dy/dx = e^(x+y) and dy/dx = e^(x-y), and find their general solutions.

## General Solution of dy/dx=ex+y

Answer: The general solution of the differential equation dy/dx=ex+y is given by ex+ e-y= C, C is an integration constant.

Proof:

The given differential equation is

$\dfrac{dy}{dx}=e^{x+y}$

By the rule of indices, the above equation can be rewritten as follows:

$\dfrac{dy}{dx}$ = ex ey

Now, separating the variables we obtain that

e-y dy = ex dx

Integrating, ∫e-y dy = ∫ex dx + K

⇒ – e-y =ex + K

⇒ ex+ e-y= C, where C=-K.

Therefore, the solution of dy/dx=e^x+y is equal to ex+ e-y= C, where C denotes a constant.

General solution of dy/dx=sin(x+y)

General solution of dy/dx=x/y

General solution of dy/dx=y/x

## General Solution of dy/dx=ex-y

Answer: The solution of dy/dx=ex-y is equal to ex– ey= C, C is any constant.

Proof:

We have:

$\dfrac{dy}{dx}=e^{x-y}$

⇒ $\dfrac{dy}{dx}$ = ex e-y

⇒ ey dy = ex dx

⇒ ex dx – ey dy = 0

Integrating both sides of the above equation, we obtain that

∫ex dx – ∫ey dy = C

⇒ ex– ey= C

So the solution of dy/dx=e^x-y is ex– ey= C, where C stands for an arbitrary constant.

## FAQs

### Q1: What is the general solution of dy/dx=ex+y?

Answer: The general solution of dy/dx=ex+y is ex+e-y=C.

### Q2: What is the general solution of dy/dx=ex-y?

Answer: The general solution of dy/dx=ex-y is ex-ey=C.