7: Wronskian Determinant - Dissecting Differential Equations

[@MuPrimeMath]

If you aren't familiar with how the determinant relates to linear independence, check out my video on determinants: th-cam.com/video/A9eJdQt5quw/w-d-xo.html

[@bijoythewimp2854]

This guy's video's always wipe my math tears and leaves youtube happily.

[@omegapolar1355]

An amazing explanation of the concept.Thank You!

[@MrMyutubechannel]

Was looking for the intuition about how this works. Thank you for the awesome explanation! Good video

[@shandyverdyo7688]

Hey, sometimes please to make a video about green's function and its application
For ODE and PDE.
It's a very rare topic on TH-cam.

[@soccerbels7947]

Ye unfortunately, the higher you go in math the hardest is to find resources

[@agnespalfi6162]

Incredibly helpful, thanks a lot!

[@souvikroy9599]

How to use Wronskian to check linear dependence of functions with more than 1 variable?
Should we use partial derivatives in the matrix for different variables??

[@schweinmachtbree1013]

0:56 homogeneous linear*

[@rodrigo454]

Awesome explanation! Tks

[@tiaanjansevanrensburg2762]

Damnnn you are awesome, Thank you.

[@tgeofrey]

Thank you

[@user-nr5tp2jo3u]

Wronskian Determinant is only working for differentiable functions. It doesn't for continous functions, therefore wee must know other ways to define linear dependence.

[@adialex1000]

the absolute function is not differentiable everywhere, So how can we differentiate it?

[@MuPrimeMath]

We can differentiate it everywhere except for at 0 and only consider those values!

[@adialex1000]

@@MuPrimeMath thanks for the video and the quick reply you have been very helpful!

[@schweinmachtbree1013]

the example doesn't work. but if you multiply both functions by x, giving x|x| and x^2, then you get a correct example (because x|x| = sgn(x) * x^2 is differentiable, unlike |x| = sgn(x) * x)

[@MuPrimeMath]

@@schweinmachtbree1013 that's a great example!

[@MathPhysicsFunwithGus]

GREAT VERY HELPFUL

[@Invalid571]

What if one of our equations, lets say g(x), is equal to e^x?

[@MuPrimeMath]

It's still possible for the Wronskian to be nonzero in that case!

[@mnasm007]

Awesome

[@jrbros2371]

More vids pls 🥺

[@AmeerHamza-cy6km]

how u solve for x, x-1, x+3

[@redwanburkan4790]

Well, u can first start with computing the wronskian. You will get 0 as a result and that's bcuz u have the third row to be zeros
However, we cannot yet conclude whether they're dependent or independent unless we check if their constant multiple can be zero.
And fortunately, they can be!
Because if you try to multiply the first function by 4, the second function by -3 and the third one by -1, then you'll end up having zero ✨