Solving A Golden Differential Equation

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[@SyberMath]

To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/SyberMath. You’ll also get 20% off an annual premium subscription.

[@barberickarc3460]

A pretty nice and basic 2nd order DE, though it would be cool to see some non homogeneous stuff. Also congrats on the sponsor ❤
Edit for the sake of clarification: an example would be:
y''+y'=y+sin(x)e^(2x)
You just need to do a quick wronskian and two integrals to get the particular solution, then you glue that on to the original solution you solved for in the video and you're done 👏 this is via method of variation of parameters. Your DE practice problems inspired me to do a course in DE and now i absolutely adore them, I'd love if you could showcase more advanced aspects of DE or maybe a word problem with them?

[@SyberMath]

Nice ! Thank you for the ideas!

[@scottleung9587]

Cool - and congrats on the sponsorship once again!

[@Mathsfighters0707]

Excellent 👌

[@jos3perez98]

I got y(x) = c1*e^(-φx) + c2*e^[(φ-1)x]

[@thatonemailbox]

Haven't been here in a minute, so glad to see you getting sponsorships!

[@lazymello6778]

I had a doubt, i'll appreciate if someone answer:
How can we assume y=e^(rx) WLOG? Aren't we assuming the range of y to be (0,inf)?

[@surelyred]

Well c1 and c2 can each be negative, meaning that y can also be negative

[@bradwilliams7198]

for the a+bi channel, you might want to use a slight variation: y'-y"=y

[@broytingaravsol]

how do u consider what content to be live streaming or not?

[@terryendicott2939]

it down

[@phill3986]

👍😎👏✌️👏😎👍