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Beyond the Answer
To solve the differential equation
we can rearrange it to isolate
:
Now we can integrate both sides with respect to
:
By using the substitution method, let
, then
, thus
.
Rearranging gives us:
Therefore, the solution is
Now, apply this equation to your life! Imagine using differential equations to model real-world phenomena like population growth or radioactive decay. They mathematically represent change over time and can help predict future trends, making you a bit of a fortune teller in the process!
For instance, consider a situation like the spread of a virus; understanding the equations can help decide when to implement safety measures or when the peak might occur, potentially saving lives. Isn’t it fascinating how mathematical solutions can have practical implications?

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