Differential Equation - 2nd Order (58 of 84) Method of Variation of Parameters: Ex. 4

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In this video I will use the method of variation of parameters to find y(t)=?, of y”+y=cos(t) (example 4).
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[@OMGtornado]

Could you do an example similar to y''' + y'' = x + e^(-x) please?

[@adliwazeer]

Do we not need to have constant for the integration of u1 and u2? Or is it just added to the constant in homogeneous solution ?

[@MichelvanBiezen]

You can always add a constant to the final solution, depending on the physical situation and what the equation represents. For example if the solution represents voltage the constant would represent a DC constant added to the time varying solution.

[@tenton2000k]

Do you have variation of parameter examples where you have repeating roots?

[@MichelvanBiezen]

You can take a look but I don't think we have such an example.

[@tenton2000k]

Michel van Biezen would it be possible to have an example in the near future?

[@muhammadridhwan266]

Thank you so much sir for the lesson.. there is nothing much i can do to repay ur kindness . I pray that god will bless you , teacher

[@curtpiazza1688]

Great! 👍

[@MichelvanBiezen]

Thank you.

[@Spyrofl]

Why didn't you just use U sub for integral of cos(x)sin(x)

[@mr.feeler9313]

Can't we use the undetermined coefficient for this??

[@Chan-ux7ej]

You may, he is just showing you a different method for a particular problem. variation of parameters come in handy when we have "non-conventional' non-homogenous equations, such as 1+tan(t). This problem has cos(t), which can be easily solved with the undetermined coefficient method.

[@andreaprincielie8610]

isnt the integral of -sintcost=cos^2t/2?

[@MichelvanBiezen]

It is (1/2) cos^2(t) but if can also be (1/2) sin^2(t)

[@humamtalhami9064]

Please use color