Mathematics: Solve the equation. StartFraction dx Over dt EndFraction equals8 xt Superscript 5 An implicit solution in the form F(t,x)equalsC is nothingequalsC, where C is an arbitrary constant. (Type an expression using t and x as the variables.)

Solve the equation. StartFraction dx Over dt EndFraction

Ответ:

19cinana

18.01.2022

Mathematics

$F(x,t) = C = xe^{-\frac{4}{3}t^6}$

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dx}{dt} = 8xt^5$

We solve the above differential equation, with the help of separation of variables.

$\dfrac{dx}{dt} = 8xt^5\\\\\dfrac{dx}{x} = 8t^5~dt\\\\\text{Integrating both sides}\\\\\displaystyle\int\dfrac{dx}{x} = \int 8t^5~dt\\\\\log(x) = \dfrac{4}{3}t^6 +\log C\\\\\text{where C is constant of integration.}\\\\\log \dfrac{x}{C} = \dfrac{4}{3}t^6\\\\\dfrac{x}{C} = e^{\dfrac{4}{3}t^6}\\\\C = x e^{-\frac{4}{3}t^6}$

Solution:

$F(x,t) = C = xe^{-\frac{4}{3}t^6}$

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Ответ:

bthomas78

09.05.2021

Mathematics

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Step-by-step explanation:

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Solve the equation. StartFraction dx Over dt EndFraction equals8 xt Superscript 5 An implicit solution in the form F(t,x)equalsC is nothingequalsC, where C is an arbitrary constant. (Type an expression using t and x as the variables.)

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