I came across the following problem that says:
Consider the 2nd order O.D.E. $y''(x)+by'+cy=0,$ where $b,c$ are real constants.If $y=\exp(2x)$ is a solution,then which of the following is correct?
My Attempt: Since $y=\exp(2x)$ is a solution of the given O.D.E., it will satisfy the given O.D.E. and hence we get,$4+2b+c=0$ and now we compute $b^2-4c=b^2+c(2b+c)=(b+c)^2 \geq 0$ .option $(D)$ looks right choice.Can someone point me in the right direction? Thanks in advance for your time.