Solve the given differential equation by separation of variables. x dy/dx = 8y

Solution:

Given, the differential equation is x dy/dx = 8y

We have to solve the differential equation by separation of variables.

Now, multiply both sides by dx

x dy = 8y dx

On rewriting the equation,

dy/8y = dx/x 

By integrating,

∫dy/y = ∫8 dx/x 

log y = 8 log x + log c

log y = log (x ⁸c)

y = cx⁸

Therefore, the general solution of the differential equation is y = cx⁸.

Solve the given differential equation by separation of variables. x dy/dx = 8y

Summary:

The solution of the given differential equation dy/dx = 8y by separation of variables is y = cx⁸.