Question

The general solution of \( z = px + qy + p^2q^2 \) is

• A. \( z = ax + by \)
• B. \( z = px + qy + a^2b^2 \)
• C. \( z = ax + by + ab \)
• D. \( z = ax + by + a^2b^2 \)

Hint:

For first-order PDEs, substitute \( p = a \), \( q = b \) to form the general integral with constants.

Answer 1

The Correct Option is D

The function given is \( z = px + qy + p^2q^2 \), and we assume \( p = a \), \( q = b \) as constants (parameters of integration). So the general solution is: \[ z = ax + by + a^2b^2 \] This matches option (4).