Solve the differential equation dy/dx + 2y = 4 with initial condition y(0) = 5.
Answer and explanation
Correct answer: C. y = 2 + 3 * e^(-2x)
- Step 1: Step 1: Separate variables: dy/dx = 4 - 2y = -2(y - 2) => dy / (y - 2) = -2 dx. Integrate: ln|y - 2| = -2x + C => y - 2 = A e^(-2x) => y = 2 + A e^(-2x). Step 2. Step 2: Use y(0) = 5: 5 = 2 + A e^0 => A = 3. Thus y = 2 + 3 e^(-2x). Check: y(0) = 2 + 3 = 5; dy/dx + 2y = -6e^(-2x) + 2(2 + 3e^(-2x)) = 4. *Answer: y = 2 + 3 e^(-2x). Why not the others:** The steady-state solution as x -> inf is y = 2.
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