partial differential equation
- Thread starter gonzales
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D
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Did you finish the problem you had asked help in:
https://www.freemathhelp.com/forum/threads/differential-equation.121438
Where the problem was:
If you have found the solution to problem above, please share your work.
Can you explain how this problem is similar (or totally different) from the problem above?
Thank you for your your consideration. Actually, the final answer is second order differential equation. I need to read more about second order equation. Then I can solve them.
topsquark
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If you break it into parts like in the last problem then you would be solving a second order ordinary differential equation, not a second order partial differential equation. You should have learned how to solve these before you got to partial differential equations. You can convert this equation into another separable equation just like the last one. Use [math]C_A(x, z) = X(x)Z(z)[/math] and see where it leads to.
See what you can do with it and let us know if you get stuck.
-Dan
Thank you so much Dan, so instead of 1-x/delta in the equation what should I put?
Best
D
Deleted member 4993
Guest
Dan said:
"If you break it into parts like in the last problem then you would be solving a second order ordinary differential equation"
Did you do that? What did you get?
topsquark
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Leave it there.
The basic method is to define [math]C_A(x, z) = X(x) Z(z)[/math]. Put that into your equation and then divide by X Z and get all the z terms on one side and all the x terms on the other. Let us know what you get.
-Dan
so after that what should I do?
topsquark
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Some typos, perhaps
1) What happened to the image? It's really dark.
2) First line. What happened to "= 0"? And it's [math]\dfrac{ \partial ^2 C_A }{ \partial ^2 x}[/math].
3) Line 3. What happened to the [math]\dfrac{V}{D_{AB}}[/math]? And when you divided by XZ the second term should also contain [math]\dfrac{Z'}{Z}[/math]. The X cancels out.
Other than that it looks good. Now solve the X and Z equations. in terms of [math]\lambda[/math].
-Dan
1) What happened to the image? It's really dark.
2) First line. What happened to "= 0"? And it's [math]\dfrac{ \partial ^2 C_A }{ \partial ^2 x}[/math].
3) Line 3. What happened to the [math]\dfrac{V}{D_{AB}}[/math]? And when you divided by XZ the second term should also contain [math]\dfrac{Z'}{Z}[/math]. The X cancels out.
Other than that it looks good. Now solve the X and Z equations. in terms of [math]\lambda[/math].
-Dan
Thank you so much for your response. I don't know what should I do because I have (1-x/delta).
