The general solution of the differential equation \; dy/dx + \; x+y+1/x-3y+5 = 0 is [AP EAPCET 21 May 2025 S2]

Correct Answer is : 3(y−1)2−2(x+2)(y−1)−(x+2)2=c3(y-1)² - 2(x+2)(y-1) - (x+2)² = c3(y−1)2−2(x+2)(y−1)−(x+2)2=c

3(y-1)² - 2(x+2)(y-1) - (x+2)² = c

x² - 3y² - 4xy - 2x - 10y = c

3(y+1)² + 2(x-2)(y+1) - (x-2)² = c

x² + 3y² + 4xy + 2x + 10y = c

Correct Answer is : 3(y−1)2−2(x+2)(y−1)−(x+2)2=c3(y-1)² - 2(x+2)(y-1) - (x+2)² = c3(y−1)2−2(x+2)(y−1)−(x+2)2=c

Test Index

Differential Equations

Section: Mathematics

Question : 16 of 48

Marks: +1, -0

\; \frac{dy}{dx} + \; \frac{x+y+1}{x-3y+5} = 0

Solution:

Given,

\; \frac{dy}{dx} + \; \frac{x+y+1}{x-3y+5} = 0

\; \Rightarrow x dy - 3 y dy + 5 dy + x dx + y dx + dx = 0

\; \Rightarrow (x dy + y dx) + 5 \cdot dy - 3 y dy + x dx + dx = 0

\; \Rightarrow d(xy) + 5 dy - 3 y dy + x dx + dx = 0

Now, integrating because every term is variable separable.

x y + 5 y - \; \frac{3y^2}{2} + \; \frac{x^2}{2} + x = C

Clearly, this equation is obtained by solving option

3(y-1)^2 - 2(x+2)(y-1) - (x+2)^2 = C

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