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clc; clear; syms x(t) y(t) s x(t) = t^2 + 5 * t + 3; y_eqn = diff(y, t, 2) + 3 * diff(y, t) + 2 * y(t); x_coeffs = double(subs(flip(coeffs(x(t))))); y_coeffs = double(subs(flip(coeffs(y_eqn)))); delta = y_coeffs(2)^2 - 4 * y_coeffs(1) * y_coeffs(3); s1 = (-y_coeffs(2) + sqrt(delta)) / 2 * y_coeffs(1); s2 = (-y_coeffs(2) - sqrt(delta)) / 2 * y_coeffs(1); dx(t) = diff(x, t); eqn = y_eqn == dx(t); Dy = diff(y, t); cond = [y(0) == 2, Dy(0) == 3]; sol = dsolve(eqn, cond)

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