Second order differential equation

[lumpyduster]

Homework Statement

So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!)

I am asked to solve this differential equation:

y''+y'-2y=0

Homework Equations

I know for a second order differential equation I can solve for the roots first. If there is one root then the solution will take the form y=c₁e^rx+c₂xe^rx

If there are two distinct roots I will get something like:
y=c₁e^r₁x+c₂e^r₂x

The Attempt at a Solution

I tried to find the roots

r²+r-2=0
r= -2 and r=1

So I get:

y=c₁e^-2x+c₂e^x

I am pretty sure this is correct (I checked to see if I got zero if I did y''+y'-2y and I did), but is there a way to find c1 and c2?

 

[SteamKing]

Homework Statement

So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!)

I am asked to solve this differential equation:

y''+y'-2y=0

Homework Equations

I know for a second order differential equation I can solve for the roots first. If there is one root then the solution will take the form y=c₁e^rx+c₂xe^rx

If there are two distinct roots I will get something like:
y=c₁e^r₁x+c₂e^r₂x

The Attempt at a Solution

I tried to find the roots

r²+r-2=0
r= -2 and r=1

So I get:

y=c₁e^-2x+c₂e^x

I am pretty sure this is correct (I checked to see if I got zero if I did y''+y'-2y and I did), but is there a way to find c1 and c2?

Not unless you have some initial values to work with, such as y(0) = 0 and y'(0) = 0. You'll need two initial values to determine c₁ and c₂.