Problem 119
Find the complete integral of p = sin q
Find the complete integral of \[ p = \sin q. \]
Explanation of Method
Set $q=a$, solve for $p$, integrate.
Step 1 · Set $q=a$ and integrate
\[ p=\sin a \implies z = \int\sin a\,dx+\int a\,dy = x\sin a+ay+b. \]
Verification
$p=\sin a$, $q=a$, so $\sin q=\sin a=p$. \checkmark
Result
The complete integral is:
\[ \boxed{ z = x\sin a+ay+b } \]