. Find the general solution to = y-t+(y-t) +1 and draw a graph of the solutions...
please answer fast For the differential equation = (y + 1)(3-y), (a)Find the steady stat solutions and inflation points of your solution curve y(t) (b)Draw the graph of glu) vs. y, where g(u)Your steady stats and stability arrows must be indicated on the graph- (c) Draw the solution curve y(t for initial value problem y(0)4, vith proper concavity, asymptotic behavior and points of inflection. For the differential equation = (y + 1)(3-y), (a)Find the steady stat solutions and inflation points...
5. Find the general solution of the inhomogeneous equation ty"- (t +1)y+y given that 1 (t) e 2 (t) t+1
Q4 a) Find the general solution of the differential equation Y') + {y(t) = 8(6+1)5; 8>0. Y'8 8 >0. 8(8-1)3 b) Find the inverse Laplace transform y(t) = £ '{Y(3)}, 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, for t > 0. You may use the above results if you find them helpful....
Find the general solution by looking for solutions of the form , where r is a real or complex constant. Use the Equations of EULER-CAUCHY y(t) = + 12" + ty' +y=0,t> 0
(17 points) (a) Find the general solution of the differential equation y" (t) + 36y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (1) y(0) = 0,7(0) = 1: y= (ii) y(0) = 1, y'(0) = 0: y= (ii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1:y= 1 (On a sheet of...
(17 points) (a) Find the general solution of the differential equation y" (t) + 4y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (i) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1, y'(0) = 0:y= (iii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1: y = (On a...
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...
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) = _______
3. Given that yı(t) = t, y(t) = t, and yz(t) = are solutions to the homogeneous differential equation corresponding to ty" + t'y" – 2ty' + 2y = 2*, t > 0, use variation of parameters to find its general solution.
ters) SUIVe y + y - Sez. Find the general solution to ty" + 3ty' +y = 0 given that yı = t-1 is one solution. 1x , ,- 8+ (0) - 1 10 _1