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4. Consider the differential equation y' - 6y' + 9y = 4e3t a) Find the general solution of the differential equation. b) Solve the IVP: Y" - 6y' +9y = 4e3with y(0) = 1 and y'(0) = 10.
Find a general solution to the differential equation. y'' – 6y' +9y=t-5e3t The general solution is y(t) =
Find a general solution to the differential equation. y'' - 6y' +9y=t-7e3t The general solution is y(t)=.
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 =
1. (each 5pts) Find the solution of the following differential equations. (a) y" + 6y' +9y=0 which satisfies yo)= 4 and V = 4 (b) v- 5y' +6y=0 which satisfies y(o)=1 and y (0)=2
given that y1= e3x is a solution, if we use the reduction of order to solve the ODE y" + =6y'+9y=0 we find that u Ax+B Ax+B)e-3x) -3x e Ax
[Second Order DE’s] Find the particular solution to y" + 6y' + 9y = 9t2 + 5. using your choice of method.
(1 point) Find a particular solution to y" + 6y' + 9y = –2e-31 yp = (-te^(-3t)/3+(1/9)-(e^-3t)/(9)-t^2e^-(3t))
(4) Consider the IVP 9y" + 6y' +2y = 0, y(37) = 0, y/(3x) = }: a) Determine the roots of the characteristic equation. b) Obtain the general solution as linear combination of real-valued solutions. c) Impose the initial conditions and solve the initial value problem.