TS EAMCET · Maths · Differential Equations
The solution of the differential equation \(\frac{d y}{d x}=\frac{y}{x}+\frac{\phi(y / x)}{\phi^{\prime}(y / x)}\) is
- A \(x \phi\left(\frac{y}{x}\right)=k\)
- B \(\phi\left(\frac{y}{x}\right)=k x\)
- C \(y \phi\left(\frac{y}{x}\right)=k\)
- D \(\phi\left(\frac{y}{x}\right)=k y\)
Answer & Solution
Correct Answer
(B) \(\phi\left(\frac{y}{x}\right)=k x\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{d y}{d x}=\frac{y}{x}+\frac{\phi\left(\frac{y}{x}\right)}{\phi^{\prime}\left(\frac{y}{x}\right)}\) Put \(y=v x \Rightarrow \frac{d y}{d x}=v+x \frac{d v}{d x}\)…
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