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Mathematics, 20.06.2020 22:57 kendratorres200
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 β x;y = c1xβ1/2 + c2xβ1 + 115x2 β 16x, (0, [infinity])The functions xβ1/2 and xβ1 satisfy the differential equation and are linearly independent since W(xβ1/2, xβ1) = β 0 for 0 < x < [infinity]. So the functions xβ1/2 and xβ1 form a fundamental set of solutions of the associated homogeneous equation, and yp = is a particular solution of the nonhomogeneous equation.
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