Non homogeneous secondary order differential equations help

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amin11234
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I can comfortably do homogeneous ones just don't know how to use the formula for non homogeneous. Could anyone talk me through the steps as well? Thank you.

x''+0x'+400x=10

x(0)=0.15

x'(0)=0

Thank you
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mqb2766
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(Original post by amin11234)
I can comfortably do homogeneous ones just don't know how to use the formula for non homogeneous. Could anyone talk me through the steps as well? Thank you.

x''+0x'+400x=10

x(0)=0.15

x'(0)=0

Thank you
The non homogeneous is the sum of the Particular Integral and the Complementary Function (homogeneous
part). What did you get for the C.F. part, assuming the right hand side is zero?

Tbh you need a textbook/notes to talk you through the general approach.
http://epsassets.manchester.ac.uk/me.../helm/19_3.pdf
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amin11234
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(Original post by mqb2766)
The non homogeneous is the sum of the Particular Integral and the Complementary Function (homogeneous
part). What did you get for the C.F. part, assuming the right hand side is zero?

Tbh you need a textbook/notes to talk you through the general approach.
http://epsassets.manchester.ac.uk/me.../helm/19_3.pdf
Thanks for your response.

I got x=0.15cos(20t)
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mqb2766
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(Original post by amin11234)
Thanks for your response.

I got x=0.15cos(20t)
Ok now consider the PI. The right hand side is constant, so sub the PI
x(t) = C
Into the non homogeneous equation. C is a constant.What do you get for C?
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ghostwalker
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(Original post by amin11234)
Thanks for your response.

I got x=0.15cos(20t)
:holmes: Bit rusty on these, but don't you need the particular integral first, before you can assign values to the constants of the C.F, that is the "0.15" (and "0")
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mqb2766
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(Original post by ghostwalker)
:holmes: Bit rusty on these, but don't you need the particular integral first, before you can assign values to the constants of the C.F, that is the "0.15" (and "0")
Yes, that was coming next :-)
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amin11234
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(Original post by mqb2766)
Ok now consider the PI. The right hand side is constant, so sub the PI
x(t) = C
Into the non homogeneous equation. C is a constant.What do you get for C?
I don't understand sorry. You're saying to sub x(t) into 0.15cos(20t)?
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mqb2766
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(Original post by amin11234)
I don't understand sorry. You're saying to sub x(t) into 0.15cos(20t)?
No.
For the comp!elementary function, forget about the non homogeneous term on the right of the ODE.
For the Particular integral , forget about the C.F. Solution and assume a solution which is directly related to the right hand side (non homogeneous term). Then sub it into the ODE and solve for any parameters.
Then add the PI and CF together and match with initial conditions.(this is where you determine the coefficients in the C.F. as ghostwalker mentioned).

So the right hand side of the ODE here is a constant, so assume a solution
x(t) = C
sub that into the left of the ODE and solve for C. What do you get?
Last edited by mqb2766; 4 weeks ago
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amin11234
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(Original post by mqb2766)
No.
For the comp!elementary function, forget about the non homogeneous term on the right of the ODE.
For the Particular integral , forget about the C.F. Solution and assume a solution which is directly related to the right hand side (non homogeneous term). Then sub it into the ODE and solve for any parameters.
Then add the PI and CF together and match with initial conditions.(this is where you determine the coefficients in the C.F. as ghostwalker mentioned).

So the right hand side of the ODE here is a constant, so assume a solution
x(t) = C
sub that into the left of the ODE and solve for C. What do you get?
I think i get it sort of. Would it be C=0.025?
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mqb2766
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(Original post by amin11234)
I think i get it sort of. Would it be C=0.025?
Correct as the derivative of a constant is zero. So the overall solution is PI + CF
x(t) = 0.025 + Acos(20t) + Bsin(20t)
Now match the initial conditions to get A and B.
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amin11234
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(Original post by mqb2766)
Correct as the derivative of a constant is zero. So the overall solution is PI + CF
x(t) = 0.025 + Acos(20t) + Bsin(20t)
Now match the initial conditions to get A and B.
Ok perfect, got it. Thanks a lot for the help
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