Which of the following differential equations can be solved using variable separable method.
$1. (x^{2} + y^{2}) d x - 2 x y d y = 0$
$2. (x^{2} + s i n x) d x + (s i n y) d y = 0$

Only 1

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Only 2

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Both 1 and 2

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None of the above

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Solution

The correct option is B Only 2
Look carefully at first equation. Do you think that we can separate all xs at one side and all ys on another side.
No it’s not possible for this equation. There will always be a y with dx or an x with dy. So the variables can’t be separated. So this cannot be solved by variable separable method.
Second equation: $(x^{2} + s i n x) d x + (s i n y) d y = 0$
This already has all x terms separated from all y terms. So this can be solved using variable separable method.

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Similar questions

1. (x^{2} + y^{2}) d x - 2 x y d y = 0

2. (x^{2} + sin x) d x + (sin y) d y = 0

A . (x^{2} + y^{2}) d x - 2 x y d y = 0

B . (x^{2} + s i n x) d x + (s i n y) d y = 0

2 x y d y = (x^{2} + y^{2}) d x

(x^{2} + y^{2}) d x - 2 x y d y = 0

2 x y d y = (x^{2} + y^{2}) d x .

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