The solution of the differential equation dy/dx + x/y · x²+y²-1/2(x²+y²)+1 = 0 is

Correct Answer is : x2x²x2 + 2y22y²2y2 - 3 log (x2+y2+2)(x²+y²+2)(x2+y2+2) = c

x² + y² + 3 log (x²+y²) = c

x² + 2xy - 3 log (x²+y²+2) = c

x² + 2y² - 3 log (x²+y²+2) = c

- x² - 2y² - 3 log (x²+y²) = c

Correct Answer is : x2x²x2 + 2y22y²2y2 - 3 log (x2+y2+2)(x²+y²+2)(x2+y2+2) = c

Test Index

TS EAMCET 04 May 2019 Shift 2 Solved Paper

Section: Mathematics

Question : 79 of 160

Marks: +1, -0

\frac{dy}{dx} + \frac{x}{y} \cdot \frac{x^2+y^2-1}{2(x^2+y^2)+1}

= 0 is

Solution:

Consider the differential equation.

\frac{dy}{dx} + \frac{x}{y} \left(\frac{x^2+y^2-1}{2(x^2+y^2)+1}\right) = 0

It is solved as

2y(x^2+y^2)\,dy + y\,dy + x(x^2+y^2)\,dx - x\,dx = 0

2y(x^2+y^2+2)\,dy - 4y\,dy + y\,dy + x(x^2+y^2+2)\,dx - 3x\,dx = 0

2y\,dy + x\,dx = 3\left(\frac{x\,dx + y\,dy}{x^2+y^2+2}\right)

2y\,dy + x\,dx = \frac{3}{2}\left(\frac{2x\,dx + 2y\,dy}{x^2+y^2+2}\right)

Integrate both sides,

2y^2 + x^2 = 3\log(x^2+y^2+2) + c

x^2 + 2y^2 - 3\log\left|x^2+y^2+2\right| = c

Go to Question:

Prev Question

Next Question