Question

Find the complete integral of p-q=0

Answer 1

SOLUTION

TO DETERMINE

The complete integral of p - q = 0

EVALUATION

Here the given equation is

$\sf{p - q = 0} \: \: \: ........(1)$

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

So the solution is given by

$\sf{z = ax + by + c} \: \: \: ......(2)$

Where a, b, c are constants

Now in order to get the complete integral we have to eliminate any one of the arbitrary constants.

Differentiating partially both sides of equation (2) with respect to x we get

$\displaystyle \sf{ \frac{ \partial z}{ \partial x} = p = a \: }$

Again Differentiating partially both sides of Equation (2) with respect to y we get

$\displaystyle \sf{ \frac{ \partial z}{ \partial y} = q = b \: }$

Putting these values in Equation (1) we get

$\sf{a - b = 0 \: }$

$\implies \sf{a = b}$

Hence the required complete integral is

$\sf{ z = ax + ay + c\: }$

Where a and c are arbitrary constants

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

d²y/dx² + 2dy/dx + 2y = sin hx

include complete solution ( Complementary Function + Particular Integral)

https://brainly.in/question/28609831