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QUESTION

Determine whether the equation
$\ds(2xt^2+x^2)\frac{dx}{dt}+2x^2t+1=0$ is exact. (Do NOT solve
the equation).

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ANSWER

$\ds\underbrace{(2xt^2+x^2)}_{p}\frac{dx}{dt}+\underbrace{2x^2t+1}_{q}=0\\
\frac{\partial p}{\partial t}=4xt,\ \frac{\partial q}{\partial
x}=4xt.$

These are the same so the equation is exact.





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