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

Описание к видео Reducible Second Order Differential Equations, Missing X (Differential Equations 27)

  / 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!!

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