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Solve the separable differential equation for u

d u/d t=e³ u+8 t
Use the following initial condition: u(0)=2.

User Kiran A B
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1 Answer

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Final answer:

The solution involves separating variables of the differential equation, integrating both sides, and then applying the initial condition to find the specific solution for u(t).

Step-by-step explanation:

To solve the separable differential equation du/dt = e^3u + 8t with the initial condition u(0)=2, we'll separate variables and integrate both sides. First, rewrite the equation as du/(e3u) = dt, since the term 8t can be treated as a separate integration with respect to t. Integrate both sides to find the antiderivatives:

  • For the left side: ∫ du/(e3u)
  • For the right side: ∫ (8t dt)

After integrating, apply the initial condition to solve for the integration constant. This will give you the explicit equation for u(t).

User SneakyShrike
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