WBJEE · Maths · Differential Equations
The general solution of the differential equation \(\left(1+e^{\frac{x}{y}}\right) d x+\left(1-\frac{x}{y}\right) e^{x / y} d y=0\) is\((C\) is an arbitrary constant \()\)
- A \(x-y e^{\frac{x}{y}}=C\)
- B \(y-x e^{\frac{x}{y}}=C\)
- C \(x+y e^{\frac{x}{y}}=C\)
- D \(y+x e^{\frac{x}{y}}=C\)
Answer & Solution
Correct Answer
(C) \(x+y e^{\frac{x}{y}}=C\)
Step-by-step Solution
Detailed explanation
\(\left(1+e^{\frac{x}{y}}\right) d x+\left(1-\frac{x}{y}\right) e^{x / y} d y=0\) \(\Rightarrow \quad\left(1+e^{x / y}\right) d x=-e^{x / y}\left(1-\frac{x}{y}\right) d y\) \(\Rightarrow \quad \frac{d x}{d y}=\frac{-e^{x / y}(1-x / y)}{\left(1+e^{x / y}\right)}\) ...(i) This is…
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