I have absolutely no idea how to solve these:
1. (x doesNOT equal 0) satisfies the equation
2.y=xe^-x satisfies xy^(1st derivative)= (1-x)y
3. y=xe^-x^2/2 satisfies xy^(1st derivative)= (1-x^2)y
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You should calculate the derivatives and then plug them into the given equations to see if they are satisfied. For y=1/x, you have
Just substitute these into the equation. It works.
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