WBJEE · Maths · Differential Equations
Let \(f\) be a differential function with \(\lim _{x \rightarrow \infty} f(x)=0\). If \(y^{\prime}+y f^{\prime}(x)-f(x) f^{\prime}(x)=0, \lim _{x \rightarrow \infty} y(x)=0\) then
- A \(y+1=e^{f(x)}+f(x)\)
- B \(y+1=e^{-f(x)}+f(x)\)
- C \(y+2=e^{-f(x)}+f(x)\)
- D \(y-1=e^{-f(x)}+f(x)\)
Answer & Solution
Correct Answer
(B) \(y+1=e^{-f(x)}+f(x)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{d y}{d x}+y f^{\prime}(x)=f(x) f^{\prime}(x) \\ & \text {I.F }=e^{\int f^{\prime}(x) d x}=e^{f(x)} \\ & \text {y. } e^{f(x)}=\int e^{f(x)} f(x) f^{\prime}(x) d x \end{aligned}\)…
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