I have absolutely no idea how to solve these:

SHOW THAT

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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- Feb 23rd 2009, 04:22 PMroksteadyDerivative HELP
I have absolutely no idea how to solve these:

SHOW THAT

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 - Feb 23rd 2009, 04:38 PMccross
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

y'=-1/x^2

y''=2/x^3.

Just substitute these into the equation. It works.