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Question

Which of the following differential equations can be solved using variable separable method.
1. (x2+y2)dx2xydy=0
2. (x2+sinx)dx+(siny)dy=0

A
Only 1
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B
Only 2
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C
Both 1 and 2
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D
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 x's at one side and all y's on another side.
No it’s not possible for this equation. There will always be a y associated with a dx or a x associated with dy. So the variables can’t be separated. So this cannot be solved by variable separable method.
Second equation: (x2+sinx)dx+(siny)dy=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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