Recent content by Kanashii

Homework Statement Consider the initial value problem x" + x′ t+ 3x = t; x(0) = 1, x′(0) = 2 Convert this problem to a system of two first order equations and determine approximate values of the solution at t=0.5 and t=1.0 using the 4th Order Runge-Kutta Method with h=0.1. Homework Equations...

Homework Statement Develop aprogram that will determine the second derivative of pi(16 x^2 - y^4) at y=2 with step sizes of 0.1, 0.01, 0.001…. until the absolute error (numerical-analytical) converges to 0.00001. Use the 2nd order Central Difference Formula. User Input: y, tolerance Output: h...

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Any solution will do? ooohhh I have tried substituting what I got from my solution into the DE. xp = 1/2 te^t - t - 1/4 e^t xp` = 1/2 (te^t + e^t) - 1 - 1/4 e^t xp`` = 1/2 (te^t + 2e^t) - 1/4 e^t 1/2 (te^t + 2e^t) - 1/4 e^t - ( 1/2 te^t - t - 1/4 e^t) = (1/2 te^t + 3/4 e^t) - (1/2 te^t - t -...

trial solution: x= e^mt x` = me^mt x`` = m^2 (e^mt) x`` - x = 0 m^2 (e^mt) - e^mt = 0 (characteristic equation) dividing both sides by e^mt, m^2 = 1 m = 1, -1 for distinct real roots, xc = A (e^ (m1)t + B (e^ (m2)t) = A e^t + B e^-t ?

I got the formula from http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx to solve for the particular solution of the DE. In this problem, g(t) = e^t + t, y1 = e^t and y2 = e^-t . The Wronskian of these two functions: | e^t e^-t | | e^t -e^-t | = (e^t)(-e^-t)...

Homework Statement Solve for the solution of the differential equation and use the method of variation of parameters. x`` - x = (e^t) + t Homework Equations [/B] W= (y2`y1)-(y2y1`) v1 = integral of ( g(t) (y1) ) / W v2 = integral of ( g(t) (y2) ) / W The Attempt at a Solution [/B] yc= c1...

Oooohhh Thank you very much!

Homework Statement A force of 10 Newtons can stretch a spring by 0.04 m. Suppose a mass of 5 kg is attached to the lower end of the spring. We stretch the mass downward by 0.05 m from its equilibrium position and release it from rest. Determine the position of the mass relative to its...