Question

find the complete integral of √p +√q = 1​

Answer 1

Answer:

Given The complete integral of partial differential equations√p+√q=1

-Oct-2020 · 2 answers

The complete integral of partial differential ... required complete integral is given by; So p = ax + (1 - √a)^2y + c ...

Answer 2

Answer: The complete integral is $z=ax+(1-\sqrt{a})^2y+c$

Complete integral: A solution to a first-order partial differential equation that comprises the same number of arbitrary constants as there are independent variables.

Step-by-step explanation:

Step 1: Given

$\sqrt{p}+\sqrt{q}=1$

It is of the form f{p, q} = 0

Step 2: Solution of the above equation

The solution is in the form $z = ax+by+c$

where a, b, and c are constants.

Differentiating z w.r.t. x

$\frac{\partial{z}}{\partial{x}} = p = a$

Differentiating z w.r.t. y

$\frac{\partial{z}}{\partial{y}} = q = b$

Substituting value in the given equation, we get

$\sqrt{a}+\sqrt{b}=1$

Therefore,

$b = (1-\sqrt{a})^2$

Step 3: Find the complete solution

Substitute b's value in z to get the complete solution

$z=ax+ (1-\sqrt{a})^2y+c$

Where a and c are arbitrary constants.