With c as arbitrary constant the solution of the differential equation dy/dx=ky is

The solution to the differential equation dy/dx = ky is y = Ce^(kt), where C is an arbitrary constant.

Here are the steps to solve it:

1. Separate the variables: dy/y = k dx.
2. Integrate both sides: ∫dy/y = ∫k dx.
3. Apply the integral of 1/x which is ln|x|: ln|y| = kx + C.
4. Apply the exponential function to both sides to solve for y: y = e^(kx+C).
5. Simplify the equation using the property of exponents a^(m+n) = a^m * a^n: y = e^(kx) * e^C.
6. Since e^C is also a constant, we can replace it with another constant, say C': y = C' e^(kx).
7. So the general solution is y = Ce^(kt), where C is an arbitrary constant.