# Find the solution of the following Differential Equation xy'=2x+2y

Find the solution of the following Differential Equation
$x{y}^{\prime }=2x+2y$
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levurdondishav4
$x{y}^{\prime }=2x+2y$
Rewrite ${y}^{\prime }-\frac{2}{x}y=2$ the integration factor: $\mu \left(r\right)=\frac{1}{{x}^{2}}$
put the equation in the form of
${\left(\mu \left(x\right)\cdot y\right)}^{\prime }=\mu \left(x\right)\cdot q\left(x\right)$
$⇒{\left(\frac{1}{{x}^{2}}y\right)}^{\prime }=\frac{2}{{x}^{2}}$
$⇒y=-2x+{c}_{1}{x}^{2}$
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Foreckije
$x{y}^{\prime }=2x+2y$
${y}^{\prime }-\frac{2}{x}y=2$
The integration factor: $\mu \left(r\right)=\frac{1}{{x}^{2}}$
${\left(\mu \left(x\right)\cdot y\right)}^{\prime }=\mu \left(x\right)\cdot q\left(x\right)$
$⇒{\left(\frac{1}{{x}^{2}}y\right)}^{\prime }=\frac{2}{{x}^{2}}$
$⇒y=-2x+{c}_{1}{x}^{2}$
alenahelenash