Question

Solve the differential equation: (dy/dx)=(2y/x)

Answer 1

Transform the equation into a separable differential equation:

`(dx)/(x) = (dy)/(2y) \\ (1)/(2) lny=lnx + C \\ ln √(y) =lnx +C`
To get rid of the logarithmic terms, raise the terms to the exponential power:

`e^((ln √(y)) ) = e^((lnx + C))`
Since
`e^(lnx) =x`,

`√(y) =x + C` since
`e^(C)` can be considered another constant. Squaring the whole answer gives the final answer,

`( √(y) = X + C) ^(2) \\ y = x^(2) + 2Cx + C^2`