20:16 A X 9= (1) 以ล Jo Skyscanner Guwahati to Shillong from Rs696 View PREVIOUS NEXT MHT CET 2021 22th September Evening Shift 1 MCQ (Single Correct Answer) +2 -0 (4) The particular solution of the differential equation (dy)/(dx)=(y+1)/(x^(2)-x), when x=2 and y=1 is A) xy=4x-6 B xy=2x-2 Correct Answer c) xy=x-2 D xy=-x+4

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20:16 A X  9= (1) 以ล Jo Skyscanner Guwahati to Shillong from Rs696 View PREVIOUS NEXT MHT CET 2021 22th September Evening Shift 1 MCQ (Single Correct Answer)  +2  -0 (4) The particular solution of the differential equation  (dy)/(dx)=(y+1)/(x^(2)-x), when  x=2 and  y=1 is A)  xy=4x-6 B  xy=2x-2 Correct Answer c)  xy=x-2 D  xy=-x+4

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Given Differential Equation:  Given the differential equation (dy)/(dx) = (y+1)/(x^2 - x) and the initial condition x=2, y=1. We need to find the particular solution that fits this condition. Simplify Equation:  Simplify the differential equation by factoring the denominator: (dy)/(dx) = (y+1)/((x-1)x). Apply Initial Condition:  Use the initial condition to plug in x=2 and y=1 into the equation: (1+1)/((2-1)2) = 2/2 = 1. This confirms that the slope at x=2, y=1 is 1. Integrate Differential Equation:  To find the particular solution, we need to integrate the differential equation. We can separate variables and integrate: ∫dy/(y+1) = ∫dx/(x(x-1)). Exponentiate to Solve for y:  Integrate both sides: ln|y+1| = ln|x| - ln|x-1| + C, where C is the integration constant. Find Integration Constant:  Exponentiate both sides to solve for y: y+1 = C*x/(x-1). Substitute for Particular Solution:  Use the initial condition (x=2, y=1) to find C: 1+1 = C*2/(2-1), so C = 1. Finalize Solution:  Substitute C back into the equation: y+1 = x/(x-1). Solve for y: y = x/(x-1) - 1 = (x-x+1)/(x-1) = 1/(x-1). Rewrite in Terms of x:  Rewrite y in terms of x to match the answer choices: y = 1/(x-1). Multiply both sides by x: xy = x/(x-1). Simplify the Expression:  Simplify the expression: xy = x/(x-1) = x/(x-1) * (x-1)/(x-1) = x/(x-1). This simplifies to xy = x - 1.

The particular solution of the differential equation $\newline$ $\frac{dy}{dx}=\frac{y+1}{x^{2}-x}$ , when $\newline$ $x=2$ and $\newline$ $y=1$ is $\newline$ A) $xy=4x-6$ $\newline$ B) $xy=2x-2$ $\newline$ C) $xy=x-2$ $\newline$ D) $xy=-x+4$

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