Question

General solution of p=tan(px-y)

Answer 1

Answer:

p=tan(px-y)

px-y=tan^-1p

y=px-tan^-1p

which is a clairaut's differential equation, hence

in solution p=C

general solution will be :- y =Cx-tan^-1C

The end...

Answer 2

The required general solution is

$\sf y = cx + {tan}^{ - 1} c$

Given :

The equation p = tan ( px - y )

To find :

The general solution

Solution :

Step 1 of 2 :

Write down the given equation

Here the given differential equation is

p = tan ( px - y )

Step 2 of 2 :

Find the solution of the equation

p = tan ( px - y )

Which can be rewritten as

$\sf y = px + {tan}^{ - 1} p$

Which is of the form y = px + f(p)

This is of Clairauts Form

The solution will be of the form

y = cx + f(c)

Hence the required solution is

$\sf y = cx + {tan}^{ - 1} c$

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