8. An LRC circuit is used to modify V, = a. The equation, in terms of current q, is given by q" + 2 q' + 5q = a with initial conditions q(0) = 0 and q'(0) = 0.Convert the given second order differential equation into two first order differential equations and then apply the RK4 numerical recursion formula with h = 0.5. Do only one recursion where you generate the individual values of the k's and l's (they will be in terms of a) which you will use to assemble the charge at 1 = 0.5. Use four decimal point accuracy in all calculations.

8. An LRC circuit is used to modify V, = a. The equation, in terms of current q, is given by q" + 2 q' + 5q = a with initial conditions q(0) = 0 and q'(0) = 0.Convert the given second order differential equation into two first order differential equations and then apply the RK4 numerical recursion formula with h = 0.5. Do only one recursion where you generate the individual values of the k's and l's (they will be in terms of a) which you will use to assemble the charge at 1 = 0.5. Use four decimal point accuracy in all calculations.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Transform the given differential equation into an equivalent system of first-order differential…

A: Given Differential equation .Transform into system of first order differential equation .

Q: The functions {1, x, e3*} are solutions to the differential equation y" - 3y" = 0. Use the ronskian…

Q: Use Euler's method (see Python code in Blackboard) to approximate the solution of the differential…

Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: Identify the linear differential equations. Justify and show work. 1) y''=ex 2) y''= ey 3)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 25x?y" + 25xy' + y = 0

Q: Which of the following differential equation has a solution of y = C,x³ + C2x ? 4y = 3x?y' – x³y" 3y…

A: To find which option is correct: We first find y' and y'' of y = C1x3 + C2 x and then we will…

Q: 8²% Classify the partial differential equation: 6- dx² -16 <0, Hyperbolic -24 < 0, Elliptic O 240,…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: x²y" – 3xy' – 2y = 0 а.

Q: Find the general solution to the differential system: ས་ 1) dt (G) (19) (G)

A: Step 1:Step 2:Step 3:

Q: Put the differentlal equation [fzifeifo]ly> =1Ø> in stondert form Rirst, then convert it in to fi/2…

Q: Suppose m1 =4 , m2 = -5, m3= -2 are roots of multiplicity one, two and three of an auxiliary…

Q: Which of the following is a nonhomogeneous linear differential equation with constant coefficients?

Q: Transform the given differential equation or system into an equivalent system of first-order…

A: To transform a second order differential equation in which x is the dependent variable,into a system…

Q: a. x²y" - 3xy' - 2y = 0 b. 25x2y" +25xy' + y = 0

Q: solve differential equation by cauchy euler method

A: The objective here is to solve the given differential equation using Cauchy Euler method. Given…

Q: Let y'= 2xy²; y = a. (-4,4),(-∞, -4] b. (-4,4) c. (-4,00),(-4,4),[4, ∞) d. (-4,00),(4,∞), e. (-∞,…

A: Given, y'=2xy2 and y=24/(x2-16)

Q: - 2y' + x = 0

Q: If the root of an auxiliary are rı = 2+3i and r2 2-3i, the differential equation is %3D Select one:…

A: We will find out the required differential equations for given roots of auxiliary equation.

Q: Prove that the differential equation any") + an-1yn-1) + an-2y(n-2) + ...+a1y + aoy = k, %D k is a…

A: We will prove the given statement.

Q: The nth root of a number can be approximated by the recursive formula 1 A = ((n-1) R₁+ n (R₁)¹- R…

A: Given Data: The nth root of a number can be approximated by the recursive formula,…

Q: V.EVALUATION: Given the following scores: 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65. Find: 1. Qi…

A: The given data is already in ascending order: 5,7,12,14,15,22,25,30,36,42,53,65 Q1=(n+1)4thterm…

Q: Consider the following differential equation and initial value. У'3 2х — Зу + 1, у(1) 3D 8; У(1.2)…

Q: Which of the following differential equation has a solution of y = Cqx³ + C2x ? 3y = 4xy" + x²y' 4y…

Q: у" — Зу" + Зу' — у %3D х — 4е* -

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the solution of the next differential equation in therms of the Bessel functions: 4x^2 y′′ +…

A: Given differential equation .We have to solve the differential equation using Bessel function.

Q: 55. Let A(t) be the area of a tissue culture at time I and let M be the final area of the tissue…

A: As your demand we solve part b.Given that Let A(t) be the area of a tissue culture at time t and let…

Q: 2y" - Зу" + 18y' - 27у %3D 81

Q: Transform the given differential equation into an equivalent system of first-order differential…

Q: 1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential…

Q: 61. Show that the differential equations y' = 3y/x and y' = -x/3y define orthogonal families of…

Q: Initially : 1/4 (j-10) = s+10 or s = 1/4j -12.5 Then 1/2 ( j-34) = s+34 sub in the equation above…

Q: Consider the differential equation y" +y" = 3e + 4t² %3D Which of the following is NOT a solution of…

A: we will first find the solution of the given differential equation that find which of the option…

Q: Determine the Hermite differential equation's power series solution y' - 2xy' + 2ky Please write…

A: (a) For Hermite’s differential equation reduces to ……(1) Comparing (1), with ,which yields Here…

Q: he source function (the right hand side) of a differential equation whose characteristic ation has…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

8. An LRC circuit is used to modify V, = a. The equation, in terms of current q, is given by
q' + 2 q' + 5q = a with initial conditions q(0) = 0 and q'(0) = 0. Convert the given second
order differential equation into two first order differential equations and then apply the RK4 numerical
recursion formula with h = 0.5. Do only one recursion where you generate the individual values of
the k's and l's (they will be in terms of a) which you will use to assemble the charge at t= 0.5.Use
four decimal point accuracy in all calculations.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

What is the resulting differential equation after the initial substitution from the appropriate 2nd order transformation? Do not transpose terms to the other side of the equation. Continue from the solution obtained with the appropriate 2nd order transformation. Assume dy/dx > 0 and x > 0. If x = 1, C1 = 0, and C2 = 0, what is the value of y?
The differential equation obtained by eliminating the arbitrary constants A and B from the relation y = Aez + Ber is = O "- 40y + 13y =0 O " - 13y + 40y =0 O "+ 40y - 13y =0 O '+ 13y - 40y = 0 O O D
ta If Jane can finish the job in 6 hours while Jenny can finish the same job in 9 hours, how would you represent the time it takes them to finish the job if they work together?
26 (A) obtain the differential equation whose generel Solution is 4=a sinox-bcos 6t, where a aud b are arbitroy constants. (B) Solve the First ordel aliFferential equation * = 18ie, by using variable separable.
Determine the solutions of the following differential equations, LINEAR DE OF ORDER, n, CASE3and 4/METHOD OF UNDETERMINE COEFFICIENTS
What is the resulting differential equation after the initial substitution from the appropriate 2nd order transformation? Do not transpose terms to the other side of the equation. Continue from the solution obtained with the appropriate 2nd order transformation. If x = 4, C1 = -1/2, and C2 = 0, what is one possible value of y?
Solve the following partial differential equation. integration factor
شحذنتس