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dy/dx = 4x + 2

Multiply both sides by dx,

dy = (4x + 2) dx

Integrating both sides,

∫dy = ∫(4x + 2) dx

y = 4x^{2}/2 + 2x + c

y = 2x^{2} + 2x + c ------------ eqn(1)

Where c is the integration constant.

Since y(0) = 0,

0 = 2(0)^{2} + 2(0) + c

0 = 0 + c

c = 0

Thus, eqn(1) becomes:

y = 2x^{2} + 2x

**Ans A**

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