The solution of the differential equation ( x^2 + y^2 )dx = 2xydy… - Vidyadip

MCQ

The solution of the differential equation $({x^2} + {y^2})dx = 2xydy$ is

A
$x = c({x^2} + {y^2})$
✓
$x = c({x^2} - {y^2})$
C
$x + c({x^2} - {y^2}) = 0$
D
None of these

✓

Answer

Correct option: B.

$x = c({x^2} - {y^2})$

b
(b) It can be written in the form of homogeneous equation $\frac{{dy}}{{dx}} = \frac{{{x^2} + {y^2}}}{{2xy}}$

Now solve it by putting $y = vx$ and $\frac{{dy}}{{dx}} = v + x\frac{{dv}}{{dx}}$.

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