# What is a solution to the differential equation (2+x)y'=2y?

Jul 7, 2016

$y = \beta {\left(2 + x\right)}^{2}$

#### Explanation:

this is separable

$\left(2 + x\right) y ' = 2 y$

$\frac{1}{y} y ' = \frac{2}{2 + x}$

$\int \setminus \frac{1}{y} \setminus \mathrm{dy} = \int \setminus \frac{2}{2 + x} \setminus \mathrm{dx}$

$\ln y = 2 \ln \left(2 + x\right) + \alpha$

$\ln y = 2 \ln \left(2 + x\right) + \ln \beta$

$\ln y = \ln \beta {\left(2 + x\right)}^{2}$

$y = \beta {\left(2 + x\right)}^{2}$