Question

The general solution of pq=1 is ______

Answer 1

SOLUTION

TO DETERMINE

The general Solution of

$\sf{pq = 1}$

EVALUATION

Here the given partial differential equation is

$\sf{pq = 1}$

Which can be rewritten as

$\sf{pq - 1 = 0}$

This PDE is of the form f(p,q) = 0

So the PDE contains p , q only

So the required general solution is given by

$\sf{z = ax + by + c} \: \: \: - - - (1)$

Where a and b are connected by the relation f(a, b) = 0

Thus we have ab = 1

$\displaystyle \sf{b = \frac{1}{a} }$

From Equation 1 we get

$\displaystyle \sf{z =ax + \frac{y}{a} + c }$

Which is the desired solution

Where a and c are constants

FINAL ANSWER

Hence the required general solution

$\boxed{ \: \: \: \displaystyle \sf{z =ax + \frac{y}{a} + c } \: \: }$

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