TS EAMCET · Maths · Differential Equations
The solution of \(x \frac{d y}{d x}=y+x e^{y / x}\) with \(y(1)=0\) is
- A \(e^{y / x}+\log x=1\)
- B \(e^{-y / x}=\log x\)
- C \(e^{-y / x}+2 \log x=1\)
- D \(e^{-y / x}+\log x=1\)
Answer & Solution
Correct Answer
(D) \(e^{-y / x}+\log x=1\)
Step-by-step Solution
Detailed explanation
Given differential equation is \[ \begin{gathered} x \frac{d y}{d x}=y+x e^{y / x} \\ \frac{d y}{d x}=\frac{y}{x}+e^{y / x} \end{gathered} \] It is a homogeneous differential equation.…
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