Consider the differential equation x²y" – 3xy + 3y = 0. (a) Verify that y = cx + c2x' is the general solution of the differential equation. %3D (b) Determine whether there exists a solution to the...

Extracted text: Consider the differential equation x²y" – 3xy + 3y = 0. (a) Verify that y = cx + c2x' is the general solution of the differential equation. %3D (b) Determine whether there exists a solution to the boundary-value problem x² y" – 3xy + 3y = 0, y(-1) = 3, y(1) = 3. %3D %3D If so, how many solutions exist? Justify your answers.