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Q4 Find the general solution of the Cauchy Euler equation Axy + 64 = 0
Q5. If r = 2i is root of the characteristic equation of the equation v” + 24″ _ Ay’ 8y = 0 find the general solution.
06. Find the general solution of the differential equation D(D + 4)*(D? _ AD + 6)y = 0
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Q4. [25 pt] Find the general solution for the Euler-Cauchy differential equation. xy” + 3xy’ + 8y = x^2 cosec(2 ln x)
Problem 4. (2 points)Consider the differential equation:Y’ + 6y + 8y = 0.Find r1, r2, the roots of the characteristic polynomial of the equation above:r1, r2 =(b) Find a set of real-valued fundamental solutions to the differential equation above.Y1 (0) =Y2 (t) =(c) Find the solution y of the differential equation above that satisfies the initial conditions:y(0) = -1,Y(0) = -4.
Problem 6. The homogeneous equation 3(4) – 3y” + 6y’ + 28y’ + 24y = 0 has characteristic polynomial (2) P(r) = r^4 – 3r^3 + 6r^2 + 28r + 24 which factors as P(r) = (r – 2)^3(r + 2). What is the general solution to the homogeneous equation (2)? What is the general solution to y” – 3y’ + 6y’ + 28y’ + 24y = 12x + 24?
Problem 3.Consider the differential equationY’ – 2y + Sy = 0.(a) Find r1, r2, the roots of the characteristic polynomial of the equation above:r1, r2 = 1 + 2i, 1 – 2i(b) Find a set of real-valued fundamental solutions to the differential equation above.Y1(t) = e^(t)cos(t)Y2(t) = e^(t)sin(t)Find the solution y of the differential equation above that satisfies the initial conditionsy(0) = 4,Y(0) = 1.
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