Find the general solution of this ODE:
d²y/dt²+11 dy/dt+28y=-2
The solution will be of the form:
y(t)=Cy₁(t)+Dy₂(t)+yp(t)
so use C and D as the arbitrary constants.
y(t)=_______
Find the general solution of this ODE: d'y dy 242 +63 + 5y = 5t” + 7 + 8e – 3t The solution will be of the form: y(t) = Cyı(t) + Dy2(t) + yp(t) so use C and D as the arbitrary constants. g(t) = Preview
Consider the ODE below. y' + 364 = sec(62) Find the general solution to the associated homogeneous equation. Use C1 and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions vi and U2 produced by the system of equations. Let vi be the function containing a trig function and V, be the function that does not contain a trig function. You may omit absolute value signs and...
Consider the ODE below. y' + 4y sec(22) Find the general solution to the associated homogeneous equation. Use ci and C2 as arbitrary constants. y(2) Use variation of parameters to find a particular solution to the nonhomogeneous equation. State the two functions Vi and U2 produced by the system of equations. Let vi be the function containing a trig function and U2 be the function that does not contain a trig function. You may omit absolute value signs and use...
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" - y = 5t, yp(t) = -51 The general solution is y(t)= (Do not use d, D, e, E, I, or as arbitrary constants since these letters already have defined meanings.)
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y-y=18t, yp(t) -18t The general solution is y(t) = | | (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
(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....
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 5 y'' = 2y + 5 cotºx, yp(x) = 3 cotx The general solution is y(x) = (Do not use d, D, E, E, I, or as arbitrary constants since these letters already have defined meanings.)
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. 5 y"' = 2y +5 tan ºx, yp(x) = tan x The general solution is y(x) = (Do not use d, D, e, E, I, or las arbitrary constants since these letters already have defined meanings.)
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" + 5y + 6y = 24x2 + 40x +8+ 12 e*. Yp(x)= e* + 4x? The general solution is y(x) = 0 (Do not use d, D, e, E, I, or las arbitrary constants since these letters already have defined meanings.)
First-Order ODE (a) .Find the general solution of the following ODE: (b). Find the general solution (for x > 0) of the ODE : Hint: try the change of variables u ≜ x, v ≜ y/x. (c). Find the solution to the ODE that satisfies y(2) = 15. Hint: Try separation of variables. For integration, try partial fraction decomposition. 2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...