Consider the initial value problem y'' – 2y' – 8y = 0, y(0) = a, y'(0) = 6 Find the value of a so that the solution to the initial value problem approaches zero as t + oo Q = a =
Find the general solution to y'' + 8y' + 41y = 0. Give your answer as y=.... In your answer, use c1 and c2 to denote arbitrary constants and the independent variable.
1) Solve the following ODE with IVP 2y" + 6y' - 8y = 0 y(0) = 4 y'(0) = -1
Find a solution 10. y" – 2y' + 2y = 2x, y(0) = 4, y'0) = 8.
Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
4. Find the solution to the differential equation y"+2y'+ 2y-S(t-) y(0) 0, y (0)-0 and graph it.
find general solution y" - 8y' + 17y = 0 is solution undamped, critically damped, over damped, or under damped?
dy Find the solution of dt = 8y (7 – y), y(0) = 21. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y =
3) Find the solution to y" -6y' +8y=16 x(0)=0, x'(0)=0 given that y.(x) = ce?* +cze** and y, (x) = 2.
(1 point) Find the general solution to y + 8y" + 25y' = 0. In your answer, use c. and.cy to denote arbitrary constants and the independent variable. help (equations)