Find the general solution of this ODE: d'y dy 242 +63 + 5y = 5t” +...
Find the general solution of this ODE:d²y/dt²+11 dy/dt+28y=-2The 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)=_______
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.)
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 differential equation: y' - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cı and ca to denote arbitrary constants. Enter ci as c1 and ca as c2. Yc = cle cle5x - + c2 b. Apply the method of undetermined coefficients to find a particular solution. yp er c. Solve the initial value problem corresponding to the initial conditions y(0) = 6 and y(0) = 7. Give...
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" + 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.)
Solve the separable ODE y'=y(7.5-5y) for a population growth model, find the general solution for the ODE and check the solutions validity.
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.)
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
8. Use variation of parameters to find the general solution of the ODE day dy daca da 2y = ce2x