How to Verify the Differential Equation y(x^2+2) - 2x dy/dx + x^2 d^2y/dx^2 = 0?

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SUMMARY

The discussion focuses on verifying the differential equation y(x^2 + 2) - 2x dy/dx + x^2 d^2y/dx^2 = 0, with the specific function y = xsin(x). The solution involves applying the product rule to find the first derivative dy/dx and the second derivative d^2y/dx^2. Participants confirm that substituting these derivatives into the left-hand side of the equation leads to a valid proof of the equation.

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maobadi
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Guys can you help me solve this please
if y = xsinx prove that
y(x2+2)-2x dy/dx+x2 d2y/dx2= 0
 
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Welcome to PF!

maobadi said:
if y = xsinx prove that
y(x2+2)-2x dy/dx+x2 d2y/dx2= 0

Hi maobadi! Welcome to PF! :smile:

Find dy/dx using the product rule, then find d2y/dx2, and then plug them into the LHS. :wink:
 
tiny-tim
Thanks for the tips and I think I have solved it.
 

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