John Haynes
01/04/2023 · Junior High School
3. Find the solution of the equation \( z=\frac{1}{2}\left(p^{2}+q^{2}\right)+(p-x)(q-y) \) which passes through the \( x \)-axis. [7 Marks 4. Verify that: \( 2 y z d x+z x d y-x y(1+z) d z=0 \) is integrable. Hence solve.
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For Problem 3, set \( z = 0 \) in the equation and rearrange to find a relationship between \( p \), \( q \), \( x \), and \( y \). For Problem 4, verify the integrability of the given differential equation and solve it if it is not exact.
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