Differential Equations

Reducible Second Order Differential Equations, Missing X (Differential Equations 27)

https://www.patreon.com/ProfessorLeonard

How to solve Second Order Differential Equations by Reducing the order with a substitution. This particular technique is valid for equations missing the ‘X’ variable.

As far as the mistake on the video (example 1): Here is the worked out solution from the point of the Mistake

1/c arctan(y/c) = x + d — I’m using ‘c’ for ‘c sub 2’ and ‘d’ for ‘c sub 3″

Multiply by ‘c’ —– arctan(y/c) = cx + cd

Tangent on both sides —– y/c = tan( cx + cd)

Multiply by ‘c’ —- y = ctan( cx + cd)

Note!!! ‘cd’ is STILL a constant —- call it ‘B’ and call the constant ‘c’ “A”

So we have —- y = Atan(Ax + B)

Hope this helps!!