Pregunta
Solve the differential equation
for a constant growth rate
.
Ask by Wyatt Ross. in South Africa
Dec 09,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The general solution to the differential equation
is
, where
is a constant.
Solución

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Como
Bonus Knowledge
To solve the differential equation
, we start by separating the variables. This involves rewriting the equation as:
Next, we integrate both sides. The left side with respect to
gives us:
And integrating the right side with respect to
gives:
Now, combining these results and simplifying leads to:
where
. To eliminate the logarithm, we exponentiate both sides:
Letting
, which is a positive constant, we have:
Thus, the solution to the differential equation
is:
where
is determined by initial conditions if provided.

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