COMEDK · Maths · 32. Differential Equations
The general solution of the differential equation \((x-y) d y=(x+y) d x\) is
- A \(\tan ^{-1}\left(\dfrac{y}{x}\right)=x^2+y^2+c\)
- B \(\tan ^{-1}\left(\dfrac{y}{x}\right)=c \sqrt{x^2+y^2}\)
- C \(e^{\tan ^{-1}\left(\dfrac{y}{x}\right)}=c \sqrt{x^2+y^2}\)
- D \(e^{\tan ^{-1}\left(\dfrac{y}{x}\right)}=\dfrac{c \sqrt{x^2+y^2}}{x}\)
Answer & Solution
Correct Answer
(C) \(e^{\tan ^{-1}\left(\dfrac{y}{x}\right)}=c \sqrt{x^2+y^2}\)
Step-by-step Solution
Detailed explanation
The given differential equation is \((x-y) dy = (x+y) dx\), which can be written as \(\dfrac{dy}{dx} = \dfrac{x+y}{x-y}\). This is a homogeneous differential equation. Let \(y = vx\), then \(\dfrac{dy}{dx} = v + x \dfrac{dv}{dx}\). Substituting these into the equation, we get…
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