Differential equation in the form of G(ax+by), intro and example

[@anuraagrapaka2385]

can you please make more videos on differential equations, require it for JEE! i absolutely love the way you teach!

[@zzwag]

Thank you so much again for all these diff eq videos!!!

[@blackpenredpen]

you're welcome! more are on the way!

[@askog1900]

How do you know what to set v to?

[@holyshit922]

Other way is solve as Riccati with paticular solution y_{1}(x)=-1/9(3x-3xsin(2sqrt(3)x)-sqrt(3)cos(2sqrt(3)x))/(1-sin(2sqrt(3)x)) I firstly found complex paticular solution and later the real one

[@mahonalukuna3351]

Good sir!!!!!!!

[@dimateo9800]

Woooooooow!!!!!!!! This was really helpful, I feel like I have been wasting money and time with my private teacher

[@demenion3521]

does this work in general for, say, integrable functions G? (or sufficiently nice)

[@XxFWLxX311]

Also, was it possible to solve as a homogeneous ODE? All terms were to the power of 2 I noticed.

[@holyshit922]

No this is Riccati and you can find particular solution but he showed a little bit easier way to solve it

[@holyshit922]

@Ranniere Ramirez I can't see this is homogeneous ODE There is no second degree term multiplied by derivative and substitution for homogeneous may not work For example if there was x^2dy/dx-x^2-6xy=9y^2 you would be able to solve it as homogeneous ODE but this ode is in Riccati form and for me Riccati equation is alternative way to solve it If you want to solve this equation as Ricatti I found this particular solution y_1(x)=-1/3x+sqrt(3)/9*cos(2*sqrt(3)x)/(1-sin(2*sqrt(3)*x)) Riccati ODE is difficult to solve in general but once we have particular solution given or it is some way found Riccati ODE becomes easy to solve

[@trooperpompeu]

He said v, all that i understand is the greek leter fi, lol