For the equation xy - xy' = 0, find two solutions, show that they are linearly...

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For the equation x²y" - xy' = 0, find two solutions, show that they are linearly independent and find the general solution. Hint: Try y = x". Equations of the form ax²y" + bxy' + cy=0 0 are called Euler's equations or Cauchy-Euler equations. They are solved by trying y = x" and solving for r (assume that x > 0 for simplicity). X For the equation x²y" - xy' = 0, find two solutions, show that they are linearly independent and find the general solution. Hint: Try y = x". Equations of the form ax²y" + bxy' + cy=0 0 are called Euler's equations or Cauchy-Euler equations. They are solved by trying y = x" and solving for r (assume that x > 0 for simplicity). X

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