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drek231 [11]
3 years ago
13

Solve the separable differential equation dtdx=x2+164 and find the particular solution satisfying the initial condition x(0)=9

Mathematics
1 answer:
maria [59]3 years ago
3 0
\dfrac{dt}{dx} = x^2 + \frac{1}{64} \Rightarrow\ dt = \left(x^2 + \frac{1}{64}\right)dx \Rightarrow \\ \\ \displaystyle \int 1 dt = \int \left(x^2 + \frac{1}{64}\right)dx \Rightarrow \\ t = \dfrac{x^3}{3} + \frac{x}{64} + C

C = 9 because all the x terms go away.

t = \dfrac{x^3}{3} + \dfrac{x}{64} + 9
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Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

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2*x^3 + 19*x^2 + 59*x + 60 =  x^3 + 16*x^2 + 42*x + 9

Then we get:

2*x^3 + 19*x^2 + 59*x + 60 - (  x^3 + 16*x^2 + 42*x + 9) = 0

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x = √17 and x = -√17

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