# Thread: Can anyone help me get to the next step in second order equations?

1. ## Can anyone help me get to the next step in second order equations?

y''-3y'-10y=0, y=1, y'=10 at x=0

I know how to get it to the general equation correctly, but where do I go from there in these types of questions?

The general form is y=C1e^-2x+C2e^5x

Do I plug in x=0? That would leave C1+C2=10 which doesn't seem right....

I need to get to y(x)=__________

2. Originally Posted by operaphantom2003
y''-3y'-10y=0, y=1, y'=10 at x=0

I know how to get it to the general equation correctly, but where do I go from there in these types of questions?

The general form is y=C1e^-2x+C2e^5x

Do I plug in x=0? That would leave C1+C2=10 which doesn't seem right....

I need to get to y(x)=__________
according to your question, you have y =1 , when x=0

that gives you $\displaystyle c1+c2=1$

and you also have y'=10 when x=0

so find the derivative of $\displaystyle y={C_1}e^{-2x}+{C_2}e^{5x}$, and use $\displaystyle y'(0) = 10$ and you will get c1+c2=(some number)..

so you will have 2 equations from which you can find out c1 and c2 and complete your equation for y