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notsponge [240]
3 years ago
13

find the particular solution to the exact differentiable equation dy/dx=(2e^x)-cosx passing through the point (0,3)

Mathematics
1 answer:
lozanna [386]3 years ago
7 0

Answer:

y = 2eˣ - sin x + 1  

Step-by-step explanation:

dy/dx = 2eˣ - cos x

(0, 3)

Integrate dy/dx to find the original function.

  • y = 2eˣ - sin x + C

Solve for C by substituting the point given.

  • 3 = 2e⁰ - sin(0) + C
  • 3 = 2 - 0 + C
  • 1 = C

Now we can substitute C into the original function.

  • y = 2eˣ - sin x + 1  

This is the particular, or explicit, solution to the differentiable equation.

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