1. Q1
Q2
Q3
Express the plane that contains the points A = ( - 5, - 2,3), B = (1,1, - 4) and C = ( - 1, - 4,3) in
equational form. Your answer should have the form ax + by + cz = d where you give the specific
numeric values for a, b, c and d. An equational form is {(x, y, z) R3 | } The Initial Value
Problem: y" -6y' = 0 with y' = 16 and y' = 48 when x = 0, has general solution y = c1e6x + c2.
Give the solution to the IVP. The solution to the Initial value problem is y = The Initial Value
Problem: y " + 3 y' - 10 y = -2 with y = - 4 and y' = - 1 when x = 0, has associated
homogeneous equation y" + 3 y' - 10 y = 0 and this has general solution y= c1 e -5x +c2 e 2x.
Write down what you would try for a particular solution. Use, as needed, the Letters A, B and C
{in that order) as unknown constants and express any polymer powers only. For the particular
solution, try y =
Solution

2. 2.) r^2 - 6r = 0 so r1 =0 and r2 = 6 y = c1e^6x + c2 e^0x = c1e^6x + c2 to find c1,c2 16 = c1 +
c2 and 48 = 6c1 so c1 = 8 c2 = 8 so y = 8e^6x + 8