TS EAMCET · Maths · Differential Equations
The general solution of \(\frac{d y}{d x}+\mathrm{y} f^{\prime}(\mathrm{x})-f(\mathrm{x}) f^{\prime}(\mathrm{x})=0, \mathrm{y}\) \(\neq f(x)\) is
- A \(\mathrm{y}=f(\mathrm{x})+1+\mathrm{ce}^{-f(\mathrm{x})}\)
- B \(y=c e^{-f(x)}\)
- C \(\mathrm{y}=f(\mathrm{x})-1+\mathrm{ce}^{-f(\mathrm{x})}\)
- D \(\mathrm{y}=f(\mathrm{x})+\operatorname{ce} f(\mathrm{x})\)
Answer & Solution
Correct Answer
(C) \(\mathrm{y}=f(\mathrm{x})-1+\mathrm{ce}^{-f(\mathrm{x})}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \frac{d y}{d x}+y \cdot f^{\prime}(x)-f(x) \cdot f^{\prime}(x)=0 \\ & \Rightarrow \quad \frac{d y}{d x}+y \cdot f^{\prime}(x)=f(x) \cdot f^{\prime}(x) \\ & P=f^{\prime}(x), Q=f(x) \cdot f^{\prime}(x) \\ & I F=e^{\int P d x}=e^{\int f^{\prime}(x) d x} \\ & I…
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