# Please answer the shown questions and show detailed steps. Thanks for your work! Find the general…

Please answer the shown questions and show detailed steps. Thanks for your work! Find the general solution to: a) x^” – 4x^’ +4x = te^2t b.) y^” + y = tan^2x c.) t^2 x^”(t) + 5x(t) = 0, t0 11.) Find the general solution to x^2y^”+4 xy^’ +6y = x^3+1 if y_1 = x^2 and y_2 = x^3 are solutions to the corresponding homogeneous equation. 12.) Find a general solution for the HLDE with constant coefficients whose characteristic (auxillary) equation is a.) (r +5)^2 (r -2)^3 (r^2+1)^2 = 0 b.) r^4(r-1)^2 (r^2+2r+4) = 0 13.) Find the general solution to y^(4) + y = (16x^4 – 11)sin (x^2)-48x^2 cos(x^2)

Please answer the shown questions and show detailed steps. Thanks for your work! Find the general solution to: a) x^” – 4x^’ +4x = te^2t b.) y^” + y = tan^2x c.) t^2 x^”(t) + 5x(t) = 0, t0 11.) Find the general solution to x^2y^”+4 xy^’ +6y = x^3+1 if y_1 = x^2 and y_2 = x^3 are solutions to the corresponding homogeneous equation. 12.) Find a general solution for the HLDE with constant coefficients whose characteristic (auxillary) equation is a.) (r +5)^2 (r -2)^3 (r^2+1)^2 = 0 b.) r^4(r-1)^2 (r^2+2r+4) = 0 13.) Find the general solution to y^(4) + y = (16x^4 – 11)sin (x^2)-48x^2 cos(x^2) on (0, infinity) if y_p = sin(x^2) 14.) Find the differential operator that will annihilate the given function: a.) x^2 -2x +5 b.) e^3x + x – 1 c.) x sin2x d.) x^2 e^-2x cos3x e.) x^2 -2x +xe^-x +sin 2x – cos3x. 15.) Find the largest interval over which the IVP y^”+1/x-3 y^’ + squareroot xy = ln x, y(1) = 3, y^'(1) = -5 [Will the IV x^2z^”+xz^’ +z = cos x, z(0) = 1, z^’ (0) = 0 have a unique solution on any interval on any interval containing the origin? Explain.] 16.) Solve the IVP: y^”‘ -y^’ = 0, y(0) = 2, y^’ (0) = 3, y^” (0) = -1

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