Pregunta
1d the general solution of the differential
Ask by Herrera Stanley. in the United States
Jan 27,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The general solution is
.
Solución
To solve the differential equation:
we can integrate both sides with respect to
:
Let’s evaluate the integral:
Let’s use substitution:
- Let
. - Then,
, which implies .
Substituting into the integral:
Therefore, the general solution to the differential equation is:
where
is an arbitrary constant.
Final Answer:
After simplifying, a general solution is –eᶜᵒˣ plus a constant. Thus,
y = − e^{cos x} + C
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Como
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Bonus Knowledge
To solve the differential equation
, we integrate both sides with respect to
. The integral of the right-hand side can be simplified:
Using substitution, let
, then
or
. Therefore, the integral becomes:
Thus, the general solution is:

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