I need a help to solve these four calculus questions.

1.

(2 marks) Find a particular solution, yp (), of the non-homogeneous differential equation d2 da2 y (2) + 2 ( y (2) ty (20) = -2+1, given that yh (x) = Ae +Bae is the general solution of the corresponding homogeneous ODE. The form of Up (a) that you would try is O yp = ax + b O yp = aex O yp = axle x O yp = axe - O yp = ae- yp = axel Enter your answer in Maple syntax only the function defining yp (x) in the box below. For example, if your particular solution is yp (x) = 3 x + 4, enter 3*x+4 in the box. yp (2) =( 3 marks ) The general solution of the homogeneous differential equation d2 d Em) - 6 dmyr) + 9y(m) = is given by u = Aemm + 3328mm where and A and B are arbitrary constants. Let us now nd a particular solution to the non-homogeneous differential equation y (as) 6 is; (as) + 9y (3:) = 13 cos(2 :3). dm2 d3 a) What form would you take as your guess for a particular solution? C? an: sin 22 (j a sin 23: \"j 11 cos 2;}: 5: ba: c0322: .5: as: sin 22 + ba: 00329:: O a sin 2a: + b cos2m b) Find a particular solution up and enter it (of the above form , evaluating :1 and/or 1) ) in the box below. :Ia- (2 marks) During the decay of a radioactive substance, the rate of decay(the rate at which the mass is lost) is proportional to the mass present at that instant. Let M denote the mass in grams of radioactive Molybdenium-93 at time t in years after it has been introduced, where the initial amount of Molybdenium-QS was M0 = 170 9. Now M satisfies the differential equation A tii_11't4=l,:M+M0, k>0 A d211}?argonnah), k0 A %=k(MMO), k>0 dM o dt =,kM k0 dt 5: %=kT+Tr, k>0 o %=k(TTr), k