COMEDK · Maths · 32. Differential Equations
The number of solutions of \(\dfrac{d y}{d x}=\dfrac{y+1}{x-1}\), when \(y(1)=2\) is
- A one
- B infinite
- C two
- D zero
Answer & Solution
Correct Answer
(D) zero
Step-by-step Solution
Detailed explanation
The given differential equation is a first-order linear separable differential equation: \(\dfrac{dy}{dx} = \dfrac{y+1}{x-1}\). Separating the variables, we have \(\int \dfrac{dy}{y+1} = \int \dfrac{dx}{x-1}\). Integrating both sides, we get \(\ln|y+1| = \ln|x-1| + C\), which…
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