1. Elimination of arbitrary constants

$\displaystyle y = c_{1}e^{2x} + c_{2}e^{3x}$

I'm trying eliminate the constants in this equation. I took the first and second derivative, but it's not working. Any suggestions?

2. You're not going to be able to eliminate them. You will need two points that lie on the curve in order to create two equations in two unknowns that you can solve for $\displaystyle c_1$ and $\displaystyle c_2$.

3. Can't I make a matrix with the coefficients and redude it to a null matrix?

4. Originally Posted by Prove It
You're not going to be able to eliminate them. You will need two points that lie on the curve in order to create two equations in two unknowns that you can solve for $\displaystyle c_1$ and $\displaystyle c_2$.
could i make a matrix from the original equation and the derivatives: $\displaystyle \left(\begin{array}{cc}1&1\\2&3\\4&9\end{array}\ri ght)$ and work it down to a null matrix?

5. Originally Posted by greencheeseca
Can't I make a matrix with the coefficients and redude it to a null matrix?
You are stuck with the arbitrary constants unless further information is given. Perhaps you should post the whole question.

6. Originally Posted by mr fantastic
You are stuck with the arbitrary constants unless further information is given. Perhaps you should post the whole question.
the whole question is.. eliminate the arbitrary constants: $\displaystyle y = c_{1}e^2x + c_{2}e^3x$

7. Originally Posted by greencheeseca
the whole question is.. eliminate the arbitrary constants: $\displaystyle y = c_{1}e^2x + c_{2}e^3x$
I doubt that very much. Because that question makes no sense. How do you expect anyone to help if you cannot accurately post the whole question.

Perhaps the question asks you to find a differential equation such that the arbitrary constant are eliminated. In which case, the answer is $\displaystyle \displaystyle \frac{d^2y}{dx^2} - 5 \frac{dy}{dx} + 6y = 0$.

8. Originally Posted by mr fantastic
I doubt that very much. Because that question makes no sense. How do you expect anyone to help if you cannot accurately post the whole question.

Perhaps the question asks you to find a differential equation such that the arbitrary constant are eliminated. In which case, the answer is $\displaystyle \displaystyle \frac{d^2y}{dx^2} - 5 \frac{dy}{dx} + 6y = 0$.
ah, actually sorry.. i wrote the question as it appears, but you're right, that is the implied part of the question. thank you. how did you eliminate the constants? when i differentiated, i can only seem to eliminate one constant or the other but not both of them.

9. Originally Posted by mr fantastic
I doubt that very much. Because that question makes no sense. How do you expect anyone to help if you cannot accurately post the whole question.

Perhaps the question asks you to find a differential equation such that the arbitrary constant are eliminated. In which case, the answer is $\displaystyle \displaystyle \frac{d^2y}{dx^2} - 5 \frac{dy}{dx} + 6y = 0$.
ahh, never mind. i see it now. thank you, sir.