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1. (9) Find the general solution to the differential equation. 1) y" - 6y' +9y = 0 2) y" - y' - 2y = 0 3) y" - 4y' + 7y = 0
(1 point) Find the solution of Y" – 6y' +9y = 144 91 with y(0) = 2 and ý (0) = 3. 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.
Find the solution of the given initial value problem. (4) – 6y'"' + 9" = 0 y(1) = 10 + e, y' (1) = 8 + 3e3, y" (1) = 9e), y'' (1) = 27e3 y (1)
Solve the given differential equation with initial condition. y'-6y = 0, y(0) = 9 The solution is y(t) = (Type an exact answer.)
(1 point) Find y as a function of lif y" - 11y +24y = 0 y(0) - S WI) = 4 W = Remark: The initial conditions involve values at two points. Problem 4. (1 point) Find the solution to the linear system of differential equations 59x +84 -42x - 607 satisfying the initial conditions (0) = 10 and y(0) -7. = X(t) = y = Note: You can earn partial credit on this problem.
Please solve both questions please.
Solve the given initial value problem. y'"' + 11y'' + 38y' + 40y = 0 y(0)= 0, y'(0) = 10, y''(O) = - 72 y(x) = Find a general solution for the given differential equation with x as the independent variable. y(4) + 6y'' +9y = 0 A general solution with x as the independent variable is y(x) =
2. (3pts) Find the general solution of y" – 54" + 6y = 0.
(3) Solve the IVP + 6y(t) + 9 Sy()dt = 1, y(0) = 0. (4) Find a(t) that satisfies e(t) = e-t +S* sinh(t – 7)2(7) dt.
7. (10 points) Find the explicit solution to 1 94" + 6y' + y = 0 with initial condition y(0) = and y'(0) = -2