Question

The partial differential equation that can be formed from $z=ax+by+ab$ has the form $(\text{with}p=\frac{\partial z}{\partial x}\text{and}q=\frac{\partial z}{\partial y})$

• A. $z=px+qy$
• B. $z=px+pq$
• C. $z=px+qy+pq$
• D. $z=qy+pq$

Answer 1

The correct option is C $z=px+qy+pq$

Given, $z=ax+by+ab$ ... (i)
Differentiating the above eqation partially w.r.t $x$ & $y$, separately, we get
$\frac{\partial z}{\partial x}=a=p$ (say) .... (ii)
$\frac{\partial z}{\partial y}=b=q$ (say) .... (iii)
$\therefore z=px+qy+pq;$ the required differential equation