(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 (72.35 KiB) Viewed 11 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 2x²y" + 5xy' + y = 0 -1 Yc = ax + bx 2 11/2012 NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) = 4, y' (1) = 2 Yp = 2 + x 2x²y" + 5xy + y = 6x + 2 By superposition, the general solution of the equation 2x²y" + 5xy' + y = 6x + 2 is y = y + y₂ so y = ax^-1+bx^(-1/2)+2+x y = 1x^(-1)+2x^(-1/2)+2+x The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval (0,inf) The Wronskian W of the fundamental set of solutions y₁=¹ and y₂ = x ¹/2 for the homogeneous equation is W = 1/2x^(-5/2)