COMEDK · Maths · 32. Differential Equations
If \(f(x)=f^{\prime}(x)\) and \(f(1)=2\), then \(f(3)\) is
- A 6
- B \(2 e^2\)
- C \(\log 8-3\)
- D \(2 e^3\)
Answer & Solution
Correct Answer
(B) \(2 e^2\)
Step-by-step Solution
Detailed explanation
Given the differential equation \(f(x) = f'(x)\), we can write it as \(\dfrac{df}{dx} = f(x)\). Separating the variables, we have \(\dfrac{df}{f} = dx\). Integrating both sides, we get \(\ln|f(x)| = x + C\), which implies \(f(x) = Ae^x\) for some constant \(A\). Using the…
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