When you say "resistance of motion", is that a force? Because if so, your units in your equation of motion are incorrect. You'd be off by a factor of . However, you can absorb the mass into the constant k. So let's assume the equation of motion you've given us is correct. Let me re-write it for you here:
Does this form suggest anything to you? Another way of thinking about this is to take the form you're supposed to prove, and use the product rule to expand out the LHS. Then compare that with the equation I just wrote down.