Differential equuation with boundary conditions

[ookt2c]

Homework Statement

d^2T/dx^2+S/K=0 Boundary Conditions T=Tsub1 @ x=0
and T=Tsub2 @ x=L

Homework Equations

The Attempt at a Solution

d^2T/dx^2 = -(S/K) <--- intergrate to get
dT=-(S/K)dx+ C1 <--- intergrate to get
T=(-S/K)x+c1+c2
apply both boundary conditions to get
Tsub1=c1+c2

Not sure if i doing it right and if i am i don't know how to get c1 and c2
Thanks for your help
Tsub2=-(S/K)*L +c1+c2

 

[gabbagabbahey]

d^2T/dx^2 = -(S/K) <--- inter[/color]grate to get

You mean "integrate", right And you aren't integrating to get to here, you are simply rearranging your DE algebraically.

dT=-(S/K)dx+ C1 <--- intergrate to get

No,

$$\frac{d^2T}{dx^2}=-\frac{S}{K} \implies \frac{dT}{dx}=\int -\frac{S}{K}dx= -\frac{S}{K}x+C_1$$

You will need to integrate once more to get $T$

 

[ookt2c]

I meant integrate that equation to get to the next line.

And after I integrate I get: T=-(S/K)* (x^2)/2+C1+C2

Now I just plug in the boudary conditions and solve the system of equations for c1 and c2 correct?

 

[gabbagabbahey]

I meant integrate that equation to get to the next line.

And after I integrate I get: T=-(S/K)* (x^2)/2+C1+C2

Now I just plug in the boudary conditions and solve the system of equations for c1 and c2 correct?

$$\int(-\frac{S}{K}x+C_1)dx\neq -\frac{S}{K}x^2+C_1 +C_2$$

You're missing something.

 

[ookt2c]

=-S/K* x^2/2+C1x+C2

Also how do I make my equations appear like yours?

 

[gabbagabbahey]

=-S/K* x^2/2+C1x+C2

Good, now use your boundary conditions to find C1 and C2

Also how do I make my equations appear like yours?

Click on the link in my sig