Question

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

Answer 1

y = 2eˣ - sin x + 1

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.