Question

how to find orthogonal trajectories using deffential equations

Answer 1

Hey mate!

Here's your answer!!

In order to find the orthogonal family, we use the following practical steps

Step 1. Find the associated differential equation.

Step 2. Rewrite this differential equation in the explicit form.
$\frac{dy}{dx} = f(x.y)$


Step 3. Write down the differential equation associated to the orthogonal family.

$\frac{dy}{dx} = \frac{1}{f(x.y)}$


Step 4. Solve the new equation. The solutions are exactly the family of orthogonal curves.

Step 5. You may be asked to give a geometric view of the two families. Also you may be asked to find a specific curve from the orthogonal family (something like an IVP).

$hope \: it \: helps \: you..$
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