Find the general solution, y(t), of the differential equation t y" – 5ty' +9y=0, t> 0....
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =
(8 pts) In this problem you will solve the non-homogeneous differential equation y" + 9y = sec (3x) (1) Let C and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 9y = 0 is the function yn (x) = C1 yı(2) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x) + C2g(x) + C19(x) + C2 f(x). (2) The particular solution yp(x)...
Find a general solution to the differential equation. y'' – 6y' +9y=t-5e3t The general solution is y(t) =
Find a general solution to the differential equation. y'' - 6y' +9y=t-7e3t The general solution is y(t)=.
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
The general solution of the equation y 9y = 0 is y cicos(3x) C2sin(3x). Find values of ci and c2 so that y(0) = 0 and y' (0) = -6 C1 C2 Plug these values into the general solution to obtain the unique solution.
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
Find a general solution to the given differential equation. 32y" - 12y' - 9y = 0 A general solution is y(t) = 0
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
Find the general solution of the differential equation. Use C1 and C2 to denote any arbitrary constants. 1) y'(t) = y(4t3 + 1) 3) y'(t) = 18t5 – 10t4 + 8 – 2t-2 4) y"(t) = 40e5t + sin(4t)