JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(t)\) be a solution of the differential equation \(\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}\) Where, \(\alpha > 0, \beta > 0\) and \(\gamma > 0\). Then \(\operatorname{Lim}_{t \rightarrow \infty} y(t)\)
- A is \(0\)
- B does not exist
- C is \(1\)
- D is \(-1\)
Answer & Solution
Correct Answer
(A) is \(0\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}\) \(\text { I.F. }=e^{\int \alpha d t}=e^{\alpha t}\) \(\text { Solution } \Rightarrow y \cdot e^{\alpha t}=\int \gamma e^{-\beta t} \cdot e^{\alpha t} d t\)…
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