Solve the differential equation dydx 2yx x 0 Answer yx Not

Solve the differential equation dy/dx =2y/x , x > 0. Answer y(x)= Note: Use C as your constant and simplify it so it is not negated or multiplied by a nu

Solution

Separating :

dy/y = 2dx/x

Integrating :

ln|y| = 2ln|x| + C

ln|y = ln|x^2| + ln|D|

ln|y| = ln|Dx^2|

So, y = Dx^2

We are asked to use C for the constant :

So, y(x) = Cx^2 ---> ANSWER