3) Find the solution to y" -6y' +8y=16 x(0)=0, x'(0)=0 given that y.(x) = ce?* +cze**...
Find the general solution of the DE: y’’(x) + 6y’(x) + 8y(x) = 3e^(-2x) + 2x
Question 3 Find the general solution of "" - 6y" + 117' - 6-0 given that r1 = 2 is a root of the characteristic equation a)y=C22*+&+603 b) y=,22+*+ Cre" c)y=C22*+&+C22 d) -Ce2+Ce*+6633 e)y=e 28+ Ce*+C, f) None of the above. Question 4 Find the general solution of "" – 3y" - Dy' + 27y=0 given that rı = -3 is a root of the characteristic equation. a) y=C2*+Cxé* +22 b) y=Ge4+Ce**,62* c) y= 3 + x +c, d) y=C+*+Cre*+,231...
use variation of parameters to find a particular solution yp(x) y" + 6y + 8y = e2x dx + y2() San f(x)y2(x) f(x)yı(2) Recall that, yp(x) = -41(x) dr. aW(41, 42) aW(41, 42) If you use the method of undetermined coefficients you will receive zero credit.
Find a solution 9. y(3) – 6y"+11y'- 6y=0, y(0)=y'(0)=0, y"(0) = 3.
3. Find the general solution of the differential equation y” + 2y' + y = 0 (a) y=ce' +c,e* (b) y= ce" + xe * (c) y = cxe* +c,e* (d) y= ce* +C,xe" (e) y=ce?* +c,e-2 (f) y= c,e + ,xe” (g) y=cxe?* +cze 2 (h) y= c,e + ,xe 21
16 and 20 please Use this in Exercises 16-21 to find a particular solution. Then find the general solution and, where indicated, solve the initial value problem and graph the solution. 16. y' + 5y' - 6y = 6e3 17. y' – 4y + 5y = 21 18. C/ Gy" +8y' + 7y = 10e-21, y(0) = -2, y0) = 10 19. C/G Y' – 4y + 4y = et, y(0) = 2, y(0) = 0 20. y' +24' +10y...
1.Find a general solution to the given differential equation. 21y'' + 8y' - 5y = 0 A general solution is y(t) = _______ .2.Solve the given initial value problem. y'' + 3y' = 0; y(0) = 12, y'(0)= - 27 The solution is y(t) = _______ 3.Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them z"'+z"-21z'-45z = 0 A general solution is z(t) = _______
(1 point) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given the first order IVP y 0, х21 (1) Find the explicit solution on the interval 0 < x < 1 У(х) %3 (2) Find the lim y(x) = х—1 (3) Then find the explicit solution on the interval x 1 У(х) —
1) Solve the following ODE with IVP 2y" + 6y' - 8y = 0 y(0) = 4 y'(0) = -1
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x > 0), find a second linearly independent solution using reduction of order.