Quick questions on Separable differential equations: separating variables, integrating both sides, and initial conditions

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the constant of integration?

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Always include a constant after integration. It is cleaner to combine the constants from both sides into one

C

on the right.

What is newton's law of cooling?

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A body cools toward an ambient temperature

T_a

at a rate proportional to the temperature difference:

What is algebra errors when isolating

y

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When solving

y^2 = f(x) + C

for

y

, the sign of the square root is fixed by continuity with the initial condition.

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