Respuesta :

Ivka93
da/dt=-9a
t is variable. integral of -9adt= -9a*integral dt= -9a*t+c
The general form of funcion that satisfies differential equations da/dt=-9a is a=-9a*t+c

A solution of differential equation is a function which satisfies the equation.
The given equation is
[tex] \frac{da}{dt} =-9a[/tex]

This ODE (Ordinary Differential Equation) is separable.
That is,
[tex] \frac{da}{a} = -9[/tex]

Integrate to obtain
[tex]\int \frac{da}{a} =-9 \int dt \\\\ ln(a) = -9t + k \\\\ a(t) = c \, e^{-9t}[/tex]
where k, c are constants.

Answer:  [tex]a(t) = c \, e^{-9t}[/tex], c = constant.

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