HW6. Please find v1 and V2 (in differential Equation form) in the following circuits: i1t0) 1200)...
Please find V1 and V2 (in differential Equation form) in the following circuits 10 igtn Pytn) 2- Fitr) 3- btn igin Pitt) 1.
1. Find the Voltages at Nodes V1 and V2
2. Find Current through R1
3. Find The Power Delivered/Sunk by I1
4. Find the current with direction through R2
R2 W 90 15A R3 Dron 10A 30 3120
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...
3. Express each of the following in simplified Cartesian form. a) (v2- V60)0 (V2 + V65)25 (b) 21010(-1 +)0(+) 4. Find the complex number z, in Cartesian form, such that it satisfies the equation 5. Find all solutions of the equation r 160 Express any complex solutions in Cartesian form, simplified as much as possible.
3. Consider the following differential equation 0o and a series solution to the differential equation of the form a" n-0 (a) Find the recurrence relations for the coefficients of the power series. 3 marks] (b) Determine the radius of convergence of the power series. l mar (c) Write the first eight terms of the series solution with the coefficients written in terms of ao and ai 2 marks]
3. Consider the following differential equation 0o and a series solution to...
Consider the following graph: V4 V1 V2 V3 V5 and consider the following process: Initially, start at v1. • At ach time step, choose one of th and move there. vertices adjacent to your current location uniformly at random, Let pi(n), p2(n), p3(n), p4(n), p5(n) be the probability your location after n time steps is v1, V2, 03, 04, or V5 respectively. So pi(0) = 1 and p2(0) = P3(0) = p4(0) = p5(0) = 0. (a) Express pi(n+1), p2(n+1),...
ASK YOUR TEACHER Sy, find an expression for Consider the following differential equation to be solved using a power series. y" - y = 0 Using the substitution y = in terms of ck+ 1 for k = 0, 1, 2, .... no C+2 k+ 2 = + + + + 4 + + V2 = x - . + Y2 + + Find two power series solutions of the given differential equation about the ordinary point x = 0....
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
Solve the following Exact Differential EquationSolve the following Exact Differential Equation with boundary value y(-1) = 2Solve the following higher order differential equation given that y(pi/3 ) = 0, y'(pi/3 ) = 2
Please help
(1 point) In this problem we consider an equation in differential form M dx + N dy-0 (- (xy' +y)) dx + (- (x2y + x))dy 0 Find If the problem is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE otherwise find F(x,...