Differential Equations - 36 - Tricky Undetermined Coefficients Example ( t*cos(t) )

[@General12th]

I never learned matrix math. So when my Linear Algebra class rushed into using it on the *first day,* I knew I was gonna have a bad time.

[@ottodvalishvili7601]

Thanks for the videos,they are great.

[@WyrmholeWarrior]

These videos are great!

[@shivanshgupta6192]

how to check if H and P part are linearly independent or not .And if not what to do in that case?

[@TheLazyEngineer]

By H and P I am assuming you are referring to the homogeneous and particular solutions, respectively? If P can be expressed in terms of H, then P is linearly dependent with H, and that means you did something wrong because P would be a homogeneous solution (by linearity of the problem). Your P needs to be linearly independent with H.

[@mohansai4143]

Is it same for tsint

[@pipertripp]

yep. Or sin(wt). it's all basically the same approach. It's a lot of algebra. the hardest part is not making dumb mistakes.

[@MrRyanroberson1]

i need some help. i'm a bit ignorant on the one tiny piece of strategy required to do the following integral, and ive tried with u sub, i know power rule, product rule, chain, and even the derivative of square roots... how does one integrate sqrt(1-xx)dx?

[@TheLazyEngineer]

Try trig substitution

[@MrRyanroberson1]

is there a way to avoid that? and i forgot to specify that x is in the range from 0 to 1 specifically. (yeah, the area of a circle btw, by design)

[@ShreyButle]

Couldn't we just use Variation of Parameters? Is it just time consuming to do so?

[@moizarif1284]

how to find the inverse ? gauss jordon ? calculators are not allowed in my uni

[@TheLazyEngineer]

that should work!

[@moizarif1284]

thank you

[@TusharKumar-iu4nt]

Quick explanation.... Can be tricky but nonetheless very useful.

[@johi5951]

Can you do please a vid solving the multivariable integral: (int(x_1 from 0 to 1)int(x_2 from 0 to 1)int(y_1 from 0 to 1)int(y_2 from 0 to 1)(sqrt(((x_1+y_1)^2)+((x_2+y_2)^2))) dx_1dx_2dy_1dy_2) PD: A_b means "a sub b"