a) Use the method of undetermined coefficients to find a particular solution of the non-homogeneous differential equation y" + 3y + 4y = 2x cosx. (9) b) Find the general solution to xy" - (x + 1)y' + y = x² on the interval I = (0,0⁰). Given that y₁(x) = e* and y₂(x) = x + 1 form a fundamental set of solutions for the homogeneous differential equation. (10) 2. Explain, in English, the difference between the method of elimination and the method of decomposition. Specifically mention where these methods are applied, that is, what problems they can be used to solve. (2) 3. Consider the non-homogeneous system of linear differential equations dx =-5x+y+6e²¹ dt dy -=4x-2y-e²¹ dt a) Show that the complementary solution to this system is X,1)=0 [1] + + c₂ [1] * X(t)=c₁ (6) b) Hence find a general solution to this system, using variation of (10) parameters. c) Rewrite the given system of DEs as a single higher order DE.