AP EAMCET · Maths · Differential Equations
The solution of \(\frac{d y}{d x}+\frac{1}{x}=\frac{e^y}{x^2}\) is
- A \(2 x=\left(1+C x^2\right) e^y\)
- B \(x =\left(1+C x^2\right) e^y\)
- C \(2 x^2=\left(1+C x^2\right) e^{-y}\)
- D \(x^2=\left(1+C x^2\right) e^{-y}\)
Answer & Solution
Correct Answer
(A) \(2 x=\left(1+C x^2\right) e^y\)
Step-by-step Solution
Detailed explanation
Given differential equation, \(\frac{d y}{d x}+\frac{1}{x}=\frac{e^y}{x^2}\) Dividing the eqn. by \(e^y\), we get Let \(e^{-y}=v\) \(\Rightarrow \quad e^{-y} \frac{d y}{d x}=\frac{d v}{d x}\) From eqn. (i), we get \(\therefore \quad \frac{d v}{d x}-\frac{1}{x} v=\frac{-1}{x^2}\)…
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