What is the particular solution y(1) for the differential equation dy/dx = 4x^3 with initial condition y(0) = 2?

Answer Key:

3

### Solution: y(x) = \int 4x^3 dx = x^4 + C. With y(0) = 2, C = 2 ==> y(x) = x^4 + 2. At x = 1: y(1) = 1^4 + 2 = 3. Correct: 3.

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