If \(y = y(x)\) is the solution of the differential equation \(\displaystyle\frac{dy}{dx} = 3x^2 + 4x\) satisfying \(y(1) = 5\), then \(y(2)\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 18
Integrating both sides gives the general solution:
\(y = x^3 + 2x^2 + C\)
Putting x = 1, y = 5 gives the particular solution:
\(5 = 1 + 2 + C\)
\(C = 2\)
\(y = x^3 + 2x^2 + 2\)
At x = 2:
\(y(2) = 8 + 8 + 2 = 18\)