(1 point) The general solution of the homogeneous differential equation can be written as where a, b are arbitrary const

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1 Point The General Solution Of The Homogeneous Differential Equation Can Be Written As Where A B Are Arbitrary Const 1 (57.77 KiB) Viewed 35 times

(1 point) The general solution of the homogeneous differential equation can be written as where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation y = 4x²y" + 9xy' + y = 0 4x²y" + 9xy' + y = 10x + 1 By superposition, the general solution of the equation 4x²y" +9xy' + y = 10x + 1 is y = Yc + Yp So NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 8, y' (1) = 6 Y 1 -1 Yc = ax + bx 4 Yp = 1 + x The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions y₁= x-¹ and y₂ = x-¹/4 for the homogeneous equation is W =