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4. Find the solution to the differential equation y"+2y'+ 2y-S(t-) y(0) 0, y (0)-0 and graph...
The function Y(t) = t is a solution of the differential equation (t2+4)y" - 2ty' + 2y = 0. Find a real general solution of this equation.
Find the particular solution such that y=0 when t=0 of the differential equation: (dy/dt) - 2y = t
Find the general solution of the given differential equation. y" + 2y' + y = 14e-t
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
(5 points) Find the general solution to the differential equation y" – 2y + 17y=0. In your answer, use Cį and C2 to denote arbitrary constants and t the independent variable. Enter Cų as C1 and C2 as С2. y(t) = help (formulas) Find the unique solution that satisfies the initial conditions: y(0) = -1, y'(0) = 7. y(t) =
Question 7 Find the general solution of the given differential equation. y" +2y' +5y=0
3- Find the general solution of the given differential equation 3-2) y'' −2y' +y = e^t /(1+t^2)
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
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 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) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
4. Consider the differential equation +2y + 2y = cost (a) (5 points) Find the general solution to the corresponding homogeneous equa- tion. (b) (5 points) Find a particular solution, y(t), to the non-homogeneous equation. (c) (2 points) Determine the general solution to the non-homogeneous equation.