Verify that the given functions y₁(t) = t and y2(t) = te³t satisfy the corresponding homogeneous equation; then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. t²y" − t(3t+ 2)y' + (3t + 2)y = 7t³, t > 0. - NOTE: Use t as the independent variable. 1 ) = c₁t+c₂te³ − (91²4 + 91³ + 6t² + 2t)

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