How Do I Solve This Complex Differential Equation?

[vinodjoshi]

Help me to solve this equation....Urgent

Hi Friends

Can anyone tell me the solution of this equation

exp(-4Ax){D^4-8AD^3+16(A^2)D^2}+i/(constant)=0

where
i is complex no.
A is a constant
D indicates dy/dx or y'(x)

Please Reply ASAP

Thanks in Advance

vinodjoshi

 

[g_edgar]

Looks nonsensical to me. (1) If D indicates dy/dx, then there should be some function following the brace } for the operators to apply to. (2) What do you want to solve FOR?

 

[Mark44]

Hi Friends

Can anyone tell me the solution of this equation

exp(-4Ax){D^4-8AD^3+16(A^2)D^2}+i/(constant)=0

where
i is complex no.
A is a constant
D indicates dy/dx or y'(x)

Please Reply ASAP

Thanks in Advance

vinodjoshi

Notwithstanding the urgency of your request, you need to make an attempt at a solution before we can help you.

 

[Martin Rattigan]

Looks nonsensical to me. (1) If D indicates dy/dx, then there should be some function following the brace } for the operators to apply to. (2) What do you want to solve FOR?

(1) If he had said D indicates d/dx what you say would apply.
(2) Usually you'd want to find y in terms of x and the constants A and "constant". (I assume that "i is complex no." means i=\sqrt{-1}.)

 

[vinodjoshi]

Sorry friends
Let me correct this equation
The correct equation is
(exp(-4Ax){D^4-8AD^3+16(A^2)D^2}+i/(constant))y=0
Sorry for the inconvenience made

 

[Mark44]

Multiply both sides by exp(4Ax) and solve the differential equation
(D⁴ - 8AD³ + 16A²D² + Ki)y = 0

Here D = d/dx and K = 1/const.

 

[vinodjoshi]

Well Mark if you examine the equation closely, you will find exp(-4Ax) is not common in whole equation its only common for {D^4-8AD^3+16(A^2)D^2}. Then how to take care of i/(constant)?

 

[Mark44]

OK, I missed that, so what you get is (D⁴ - 8AD³ + 16A²D² + Kie^4Ax)y = 0

This is pretty messy, but at least it's linear.

 

[vinodjoshi]

Thanks for the help but can you explain how to solve it.....

 

[Mark44]

What is the original problem statement?

 

[Redbelly98]

Thanks for the help but can you explain how to solve it.....

According to Physics Forums policy, you will need to make some attempt at solving the problem yourself first. Surely there is something in your class lecture notes or textbook that is relevant. Make an attempt to share what you know, then others can help you.