If y is a function of x and z = e^z, show that: x (dy/dx) = (dy/dz) and (x^2) (d2y/dx2) = (d2y/dz2) - (dy/dz) I managed to work out the first part. But I don't know how to prove the second part. Can someone please show me how?
let d2y/dx2= 6x. Find a solution to the differential equation that is continuous for negative infinity to positive infinity and whose graph passes through the point (0,1) and has a horizontal tangent there.