9: Variation of Parameters - Dissecting Differential Equations

Video on the Wronskian determinant: • 7: Wronskian Determina...
An explanation of the variation of parameters method to solve second-order differential equations. This method is so fun to use!
Full Dissecting Differential Equations playlist: • Dissecting Differentia...
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[@haithamabdelrahman6276]

Brilliant , thanks for clarification of theory behind this method to solve second order equation

[@aeolidida3204]

Wow, you're amazing! I didn't understand why we do all of this, but now I finally get it.

[@nuklearboysymbiote]

Didn't expect to get it first try. Was surprised. You're a pro!

[@SlingerDomb]

Wow. This is amazing. Also, may I ask you to explain this method but with higher order ? And btw, thank you so much for making this video!

[@ayoubachak01]

I love your explanation amazing work

[@nathanisbored]

i dont get why we're allowed to assume a solution is of the form u(t)*y1(t).... how do we know its a function multiple of a homogeneous solution? what if it cant be written that way?

[@MuPrimeMath]

For any particular solution y_p, we could always write it as (y_p/y_1)*y_1, and there's our function multiple on the left. For constant coefficients, the complementary solutions are always exponentials and therefore nonzero. The only possible exceptions would be weird nonconstant coefficient cases where both complementary solutions are zero at some point, but the particular solution is nonzero. I can't think of an example of that off the top of my head

[@nathanisbored]

@@MuPrimeMath oh hmm, yeah i guess. cool

[@mohammadzuhairkhan8661]

When is part 10 coming?

[@MuPrimeMath]

I'm finished with this series for now, but I've also done some other differential equations videos! Here are two playlists to look at: Differential equation battles Differential Equation Battles: kzbin.info/aero/PLug5ZIRrShJFPgeyYpfKf2lazeZ3axKqX Laplace transforms Laplace Transforms: kzbin.info/aero/PLug5ZIRrShJER_zQ-IVVefmsh9vZHwGnv

[@jeffburdette2025]

Cool