Engineering Maths question Please solve questions 5-8

5. Give the form of a particular solution of y" + 4y' + 8y = 2re-2 sin 2x. (a) z = (Ax + B) e 27 cos 2x + (Cx + D) e 25 sin 2x (b) z = (Ax2 + Bx) e 2* sin 2x (c) z - (Ax2 + Bx) e 21 cos 2x + (Cx + D) e-21 sin 2x (d) z = (Ax2 + Bx) e 2x cos 2x + (Cx2 + Dx) e 2x sin 2x (e) None of the above. 6. Give the general solution of y" - 3y" - 4y' - 4x + 5. (a) y = C1+ Cze "+ Czer (b) y = C1+ Cze " + C3ex + 1x 27 - 372 (c) y = C1+ Cze " + C3ex - 2 - 1x (d) y = C1 + Cze " + Cge47 + 4 - 4x2 (e) None of the above. 7. Give the form of a particular solution of y" - 5y" + 6y' - 2xces + 4x2 + 2. (a) z = (Ax + B) e3x + Cx2 + D (b) z = (Ax2 + Bx) e3x + Ca3 + Dx (c) z = (Ax2 + Bx) e37 + Cx3 + Dx2 + Ex (d) z = Axle3x + Bx2 + Cx + D (e) None of the above. 8. Give the form of a particular solution of y" - 2y" - 8y' = 2 cos 3x - 2e -2x + 5. (a) z = Acos3x + B sin 3x + Cx2e-2x + D (b) z = Acos3x + B sin 3x + Cxe 2x + Da (c) z = Acos3x + B sin 3x + Cxe 27 + Dx + E (d) z = Axcos3x + Bx sin 3x + Ce-2x + Dx