3 4 Y 3 2 1 Consider thee equation Y' 5 |0- Find the solution with...
5. Find a solution of a IVP consisting of the DE y-2 y=cie 3 6x+4, with solution 33 + coe-2x and initial conditions 1(1) 4, y'(1)-2 6. Given a direction field, sketch by hand an approximate solution curve that passes through a given initial condition (a) y(0) 0 (b) y(0) 2 5. Find a solution of a IVP consisting of the DE y-2 y=cie 3 6x+4, with solution 33 + coe-2x and initial conditions 1(1) 4, y'(1)-2 6. Given a...
(1 point) Consider the differential equation This equation has the 2 constant solutions (in increasing order) y -3 and y= The solution of this equation subject to the initial condition y(O)9 is y- (1 point) Consider the differential equation This equation has the 2 constant solutions (in increasing order) y -3 and y= The solution of this equation subject to the initial condition y(O)9 is y-
(1 point) a. Consider the differential equation: d2y 0.16y-0 dt2 with initial conditions dt (0)-3 y(0)--1 and Find the solution to this initial value problem b. Assume the same second order differential equation as Part a. However, consider it is subject to the following boundary conditions: y(0)-2 and y(3)-7 Find the solution to this boundary value problem. If there is no solution, then write NO SOLUTION. If there are infinitely many solutions, then use C as your arbitrary constant (e.g....
3. Consider the following third order linear differential equation: y3y-4 y'-0 (a) Find the general solution. (b) Find the solution that satisfies the following initial conditions: y(0)=4, y'(0)-6, y(0)=-14 (c) Find the dominant eigenvalue, and use it to determine the long-term behavior of the solution.
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
y" – 7y' +12 y = 0, y(0) = 3, y'(0) = -2. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, y" + 10 y' + 25 y=0, y(0) = 5, y (0) = -5. a. (4/10) Find the Laplace Transform of the solution, Y(s) = L[y(t)]. Y(s) =...
1. Find the particular solution of the differential equation dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x) satisfying the initial condition y(0)=4y(0)=4. 2. Solve the following initial value problem: 8dydt+y=32t8dydt+y=32t with y(0)=6.y(0)=6. (1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...
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...
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' +...
dicated initial condition. In #4-5, find the particular solution for each differential equation given the indicated initial 4 de -cosx=0, 600)=1. s. 1-2x = 0, y(0)= In 2