TS EAMCET · Maths · Differential Equations
The solution of the differential equation \(y^{\prime}=\frac{1}{e^{-y}-x}\) is
- A \(x=e^{-y}(y+C)\)
- B \(y+e^{-y}=x+C\)
- C \(x=e^y(y+C)\)
- D \(x+y=e^{-y}+C\)
Answer & Solution
Correct Answer
(A) \(x=e^{-y}(y+C)\)
Step-by-step Solution
Detailed explanation
Given differential equation is \(y^{\prime}=\frac{1}{e^y-x}\) \[ \frac{d y}{d x}=\frac{1}{e^y-x} \] We can write this equation in the form \[ \begin{aligned} \frac{d x}{d y} & =e^y-x \\ \frac{d x}{d y}+x & =e^y \end{aligned} \] Compare Eq. (i) by \(\frac{d x}{d y}+P x=Q\), we…
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