mattgondek4

2021-02-27

Solve the following differential equations:

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

Obiajulu

Skilled2021-03-01Added 98 answers

Step 1

Given

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

To Find- The value of the above differential equations.

Step 2

Explanation- Rewrite the given expression,

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

Simplifying the above expression and integrating both sides, we get,

$\int (y+{e}^{y})dy=\int (x-{e}^{-x})dx$

$\frac{{y}^{2}}{2}={e}^{y}=\frac{{x}^{2}}{2}+{e}^{-x}+C$

$\frac{{y}^{2}}{2}-\frac{{x}^{2}}{2}+{e}^{y}-{e}^{-x}=C$

Answer- Hence, the solution of the differential equation$\frac{dy}{dx}=\frac{x-{e}^{-x}}{y+{e}^{y}}$ is

$\frac{{y}^{2}}{2}-\frac{{x}^{2}}{2}+{e}^{y}-{e}^{-x}=C$ .

Given

To Find- The value of the above differential equations.

Step 2

Explanation- Rewrite the given expression,

Simplifying the above expression and integrating both sides, we get,

Answer- Hence, the solution of the differential equation

Jeffrey Jordon

Expert2021-11-20Added 2607 answers

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