COMEDK 2025 Evening Solved Paper

Concept:This is a first‑order separable ordinary differential equation. The initial condition must be consistent with the general solution.Explanation:Separate the variables:$$\frac{dy}{y+1} = \frac{dx}{x-1}$$Integrate both sides:$$\int \frac{dy}{y+1} = \int \frac{dx}{x-1}$$$$\ln|y+1| = \ln|x-1| + C$$Exponentiate to obtain the general solution:$$|y+1| = e^C |x-1| \quad\Longrightarrow\quad y+1 = A(x-1)$$where $A$ is an arbitrary constant. Apply the initial condition $y(1)=2$:$$2 + 1 = A(1-1) \quad\Longrightarrow\quad 3 = A \cdot 0$$This gives $3=0$, which is impossible. Hence no value of $A$ satisfies the condition.Therefore, there is no solution to the differential equation with the given initial condition.Answer:zero