Solve the differential equation dy/dx=(x+y)1/(-x)

 Exercise

$\frac{dy}{dx}=\left(x+y\right)\frac{1}{-x}$

 

Multiply the fraction by the term

$\frac{dy}{dx}=\frac{1\left(x+y\right)}{-x}$

 

Any expression multiplied by $1$ is equal to itself

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

 

Expand the fraction $\frac{x+y}{-x}$ into $2$ simpler fractions with common denominator $-x$

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

 

Simplify the fraction $\frac{x}{-x}$ by $x$

$\frac{dy}{dx}=-1+\frac{y}{-x}$

$\frac{dy}{dx}=-1+\frac{y}{-x}$

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