21.
Posted: Tue Jul 12, 2022 12:00 pm
21.
We consider the non-homogeneous problem y" + 6y + 10y = 180 sin(2x) First we consider the homogeneous problem y" + 6y' +10y=0: 1) the auxiliary equation is ar² + br+c=r^2+6+10 =0. 2) The roots of the auxiliary equation are 3+1,-3-1 3) A fundamental set of solutions is obtain the the complementary solution y = 13/1 + 2/2 for arbitrary constants c₁ and ₂. y= (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we Next we seek a particular solution y, of the non-homogeneous problem y" + 6y + 10y= 180 sin (2a) using the method of undetermined coefficients (See the link below for a help sheet) 4) Apply the method of undetermined coefficients to find y₂ = -12cos(2x)+6sin(2x) We then find the general solution as a sum of the complementary solution / ye+yp. Finally you are asked to use the general solution to solve an IVP. 5) Given the initial conditions y(0)=-12 and y' (0) = 10 find the unique solution to the IVP c131 +022 and a particular solution:
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