Question

Verify y = log x + c is a solution of the differential equation

`x(d^2y)/dx^2 + dy/dx = 0`

Answer 1

y = log x + c

Differentiating w.r.t. x, we get

`dy/dx = 1/x`

∴ `x dy/dx = 1`

Again, differentiating w.r.t. x, we get

`x (d^2y)/dx^2 + dy/dx = 0`

∴ Given function is a solution of the given differential equation.