solving a hard Bernoulli differential equation

For more practice on first-order differential equations, please see my differential equation ultimate study guide 👉 • 24 First-Order Differe...
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[@Ninja20704]

I laughed when you said “my favourite integration technique called ‘wouldn’t it be nice’” I had a question in my exam that required this exact idea and i was so thankful i watched your video on the 1 2 3 4 integral you mentioned.

[@lukasstanik1107]

hello, do you happen to know the video title, please?

[@holyshit922]

Recipe for Riccati equation Pick a random functions p(x) and q(x) and u(x) Let u(x) be particular solution of Riccati equation Write Bernoulli equation with r=2 Substitute v(x)=y(x) - u(x) If we pick our favourite function for u(x) we can generate Riccati equation fe from this equation and such Riccati equation would not be difficult to solve

[@dalek1099]

You don't need the substitution though. Instead with Bernoulli Equations like dy/dx+p(x)y=y^2 you can divide by y^2 and multiply by -1 to get -y^-2dy/dx -p(x)y^(-1)=-1. Then, e integral -p(x) dx becomes the integrating factor and you will get d/dx(IF*y^-1)= -1*IF. This works on all Bernoulli equations to my understanding, so substitution is not needed. I was able to adapt the method from a textbook that seemed to bizarrely multiply by 2 when there was y^2 and I figured out what was going on. You need to generate a product rule involving y^n* IF.

[@m.selvakumar1317kanithatamili]

Superb... Awesome🎉

[@Maths_3.1415]

Nice :)

[@le0widx758]

Not tanx + 1 again 😭