Question

solution of px+qy=z is
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Answer 1

Step-by-step explanation:

For example, z=y f (y/x) is also a solution of the partial differential equation z = px + qy. This solution is different from the complete integral z = ax + by of the partial differential equation z=px+qy.

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Answer 2

The resultant general solution becomes

Ф( x/y, = 0,y/z)

Step-by-step process

Given :

Equation = px + qy =z

To find = general solution of the above equation

Solution:

The subsidiary form for the above equation will be:

dx÷x = dy÷ y = dz÷ z

Taking the first two values:

dx÷x = dy÷ y

Integrating the above mentioned equation, we get

logx = loy + log$c_{1}$

This equation becomes:

x = y ×$c_{1}$

$c_{1}$ = y ÷ x----- 1

Now, taking the second half of the equation and integrating it, we get.

dy÷ y = dz÷ z

logy = logz +log$c_{2}$

This can be written as

y = z× $c_{2}$

$c_{2}$ = z÷y--------2

Result:

Thus, the resultant general solution becomes

Ф( x/y, = 0,y/z)

Here, Ф is arbitrary

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