: It is known that y (x) = x and y2(x) = x² are solutions of the differential equation x²y" – 2xy + 2y 0. (a) Verify that y3(x) = 2x + x² is also a solution of the differential equation. (b) Use the...

Extracted text: : It is known that y (x) = x and y2(x) = x² are solutions of the differential equation x²y" – 2xy + 2y 0. (a) Verify that y3(x) = 2x + x² is also a solution of the differential equation. (b) Use the Wronskian to determine whether y1, y2 and y3 are linearly dependent on the interval (0, оо).