2) y = c. ex + cac" is a two-parameter solution of the second-order DE y"-y...
y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y' + 2xy2 = 0. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(-3) = y = Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.) Give the largest interval I over which the solution is defined for the given initial condition. (Enter your answer using interval...
In this problem, y = Ciex + c2e-X is a two-parameter family of solutions of the second-order DE y" - y = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. y(0) = 1, y'O)= 8
1 y = +c is a one-parameter family of solutions for the first order DE y' + 2xy2 0. Consider the IVP consisting of the DE with the initial value y(1) = 1/4. What is the value of c? A/
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...
Q2. X = ci cos t + C2 Sint is a two parameter family of solutions of the second order DE x” + x = 0 . Find a solution of the second order IVP consisting of this differential equation and the given initial conditions X (0) = -1 ,x' (0) = 8
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y = 3. -12 points ZillDiffEQModAp111.2.001. 0/6 Submissions Used My Notes Ask Your Teacher In this problem, y = 1/(1+ce) is a one-parameter family of solutions of the...
1. Solve by making a substitution to reduce the given second order De to a first order DE. 1. x? y" + 2xy' - 1 = 0, x>0 (ans. y = Cix-1 + 2 + In x) 2. y" + y(y')} = 0 (ans. 1/3 y3 - 2c1y + C2 = 2x) 3. y'y” = 2, y(0) = 1, y'(0) = 2 (ans. y = 4/3 (x + 1)3/2 - 1/3)
(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-
(9 points) Use the Reduction of Order Formula to find a second linearly independent solution to the DE given by xay" + 2x y' - 2y = 0, if y, (x) = x is one solution of the DE.
1. Sudden switched-on perturbation calculate ca(t) and c,(t) to second order for a two-level system with Hab, Hba independent of time and Haa H-O. Use or a two-level system WI initial conditions ca(0) 1, c(0) - 0. Sketch the probability Pa-b(t) (b) This problem can be solved exactly. Find the exact solution and compare it to your solution in part a
1. Sudden switched-on perturbation calculate ca(t) and c,(t) to second order for a two-level system with Hab, Hba independent...