Problem 3: olve the following differential equation (Bino ntial equation (Binomial series): (1+x)y' = py, IC: x = 0, y(0) = 1
Show that: olve the differential equation above by integration from T to T2 to obtain an expression would allow you to relate AA at the two temperatures.
olve the following heat problem using the method of separation of variables: lxx 6. S olve the following heat problem using the method of separation of variables: lxx 6. S
olve the quadratic equation by completing the square x2 -4x-71 0 dentify the value of "a" for the given equation. a(Type an integer or a fraction.)
2. Solve the initial value problem for the given differential equation. 2. Solve the initial value problem for the given differential equation.
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v2)y 0. (b) Find the general solution of the differential equation (y(). (You do not need to find the value:s of Gamma functions.) (c) Find the term multiplying ? in the solution. (You do not need to find the values of Gamma functions.) Problem 1. (25 points) Consider the following...
shown below. (10 points). rmine the differential equation relating vi) and vot) for the RLC circuit i(t) C-0.5 F v(t) V,(t) b.. Suppose that avo(t) vi(t) e-3t u(t). Determine vdt) for t > 0 if vo(0-)-1 and 1 t-o-=2. (10 points). at
(15 points) This problem is related to Problem 7.23-24 in the text. Given the differential equation"+20 5v (cos(9 t)u(t) Write the matrix equation for using Euler's method to compute v(t +h) from information of the function at time t, i.e., you know v(t) and initial conditions. It is assumed you will use two auxiliary functions, vi() and u2) vi(t+ h) v2(t+h vi(t) tr(t) vi (t) u2(t) For h-0.1, compute the solution for ț-0, 0.1, 0.2, 0.3, when the initial conditions...
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which has a regular singular point at x = O. The indicial equation for x = 0 is rt with roots (in increasing order) ri- Find the indicated terms of the following series solutions of the differential equation: (a) y = x,16+ and rE x+ The closed form of solution (a) is y 6: Problem 4 Previous Problem List Next (1 point) Consider the differential equation which...