Verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equat

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Verify That The Given Two Parameter Family Of Functions Is The General Solution Of The Nonhomogeneous Differential Equat 1 (12.85 KiB) Viewed 29 times

Verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval. 2x²y" + 5xy' + y = x² = x; y = ₁x² ¹/² + ₂x² ¹ + x²-1⁄x, (0,00) The functions x-1/2 and x1 satisfy the differential equation and are linearly independent since W(x-1/2, x-¹)= nonhomogeneous equation. #0 for 0 < x < 0o. So the functions x-1/2 and x-1 form fundamental set of solutions of the associated homogeneous equation, and y₂ = is a particular solution of the