Find the Wronskian of four solutions of
t^(2)y'''' − 7t^(5) y''' + 4t^(8)y'' − 5ty' + 8y = 0
Find the Wronskian of four solutions of t^(2)y'''' − 7t^(5) y''' + 4t^(8)y'' − 5ty' + 8y = 0
2. Show that if p is differentiable and p(t) > 0, then the Wronskian W(t) of two solutions of [p(t)y'l' +q(t)y = 0 is W(t) = po where c is a constant.
Two solutions to y' + 6y + 25 = 0 are y1 = = e 3t sin(4t), y2 = e cos( 4t). a) Find the Wronskian. W b) Find the solution satisfying the initial conditions y(0) = - 4, y'(0) = 0 y =
Question 2 > Solve y' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude O Oscillating with increasing amplitude
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' +...
Question 2 < > Solve y"' + 4y' + 8y = 0, y(0) = 1, y'(0) = 6 g(t) = The behavior of the solutions are: O Steady oscillation O Oscillating with decreasing amplitude o Oscillating with increasing amplitude
(1 point) Find y as a function of t if y-8y = 0, (0) - 6, (1) = 2. y(t) Remark The initial conditions involve values at two points
find y(t) solution of the ivp: y''+8y'+20y=-4£(t-2),y(0)=0,y'(0)=1 where £ is the S shaped character show work
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)
pls do all questions.
thanx
1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...
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) = _______