Question

find the complete solution of pq=4​

Answer 1

GIVEN :

The equation is pq=4​

TO FIND :

The complete solution of pq=4​

SOLUTION :

Given  equation is pq=4​

The given equation is of the form $f_1(x,p) = f_2(y,q)$

Let $\frac{p}{4}=\frac{4}{q}=k$

$\frac{p}{4}=k$

$p= k\times 4$

p=4k

$\frac{4}{q}=k$

$q=\frac{4}{k}$

The formula for Complete solution is given by :

$z=\int pdx+\int qdy$

Now substitute the values of p and q in the above formula we get,

$z=\int 4kdx+\int (\frac{4}{k})dy$

$z=4k\int dx+ \frac{4}{k}\int dy$

By using the formulae for integration

i) $\int dx=x+c$ and

ii) $\int dy=y+c$

$z=4kx+(\frac{4}{k})y+c$

∴ the complete solution of the given equation pq=4 is $z=4kx+(\frac{4}{k})y+c$

∴ the complete solution is $z=4kx+(\frac{4}{k})y+c$

or $z=4(kx+\frac{4}{y})+c$