A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 400 degrees Celsius. The ends of the bar (x = 0 and x 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u-(2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 400 degrees Celsius. The ends of the bar (x = 0 and x 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u-(2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

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: this is base on diffrenecial equation questions LINEAR EQUATIONS & EXACT EQUATIONS &…

A: falseExplanation:Step 1: Step 2: Step 3: Step 4:

Q: 1. -8--6 O {(-3, 1), (-1,0), (0, 2), (1, 4), (5,2)) {(1, -3), (-1,0), (0, 2), (4, 1), (2,5)} {(1,…

A: By looking at the given graph, the set of ordered pair corresponds to the graph are: {(1,-3),…

Q: 6. - ydx + (x ++ |xy )dy = 0

Q: Find the general solution of: (x² - y² )dx + 2xydy = 0 %3D

Q: (xe* + 6)dy + (e*y+ xe*y) dx = 0; y(0) = 8 %3D

Q: (s-s²-t²)ds + (t + s? +t ?)dt = 0 %3D

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Consider the provided question,

Q: Solve the differential equation with appropriate method (linear coefficients in two variables).…

Q: 3x * x3 - 8(y + 1) = 0 y+1 (2v2 + 4u?v)du + (4uv + 3u³)dv = 0

Q: A thin bar of length L= 3 meters is situated along the x axis so that one end is at x = 0 and the…

Q: deducted from points of correct answers. LINE 1 LINE 2 LINE 3 LINE 4 LINE S LINE G LINE 7 LINE 8…

A: Solution of the homogeneous differential equations

Q: (a) y" + 9y = 6e3¤ (b) y" – 9y = 6e3. %3D

Q: For problems #1-#4, I would suggest you use the template provided for you on Blackboard.…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Solve the following IVP and then calculate x(1.1) to the nearest thousandth (3 decimal places). Put…

Q: DIFFERENTIAL EQUATIONS Solve the following problems showing every detail of your solution.

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: We can solve this question by using Heat equation in one dimension. And the solution of ux,t by…

Q: Solve L Separate into two fractions 35 15°+7 (3s+5) 4 så +7

Q: For the differential equation y +2cos(y) y = 1

Q: Solve the differential equation dy tan dx 2y-cotx

A: Given differential equation is tan2xdydx=e2y-cotx We can write it as dye2y=dxecotxtan2x…

Q: Find one solution of the system x = 5x1 – 4e', x, = 2x1 + 3x2, xz = -x3 + 2e* -

A: We have x'1=5x1-4et ...(i) x'2=2x1+3x2 ...(ii) x'3=-x3+2et…

Q: DIFFERENTIAL EQUATIONS UPVOTE WILL BE GIVEN! Answer the following in 2-3 paraghraps. Give how…

A: Hint: Give the example where the non homogeneous linear differential equation and simultaneous…

Q: dy – 2x(x² – y)dx = 0 -

A: Given differential equation dy-2x(x2-y)dx=0 Which in the form of first order linear differential…

Q: dy %3D (x + 1 +ху + у)dx У (0) —D 5

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 00 162n-3 ac² cn 4

Q: 1. Given the equation: 1 1 + -= 1 x y (1) (a) Find by applying implicit differentiation in eq (1).…

Q: A thin bar of length L= 3 meters is situated along the x axis so that one end is at x = 0 and the…

Q: Numerical Analysis Question. xex - 37 = 0 solve by Newton Raphson method till 10 itterations or…

A: Given fx=xex-37=0

Q: olve the following equation using method of undetermined coefficients. y + y"=3x² +4 sin x–2 cosx.

Q: A thin bar of length L-3 meters is situated along the x axis so that one end is at x =0 and the…

A: Given- a thin bar of length 3 meters such that one end is at x=0 and another end is at x=3.…

Q: Solve the Application of Differential Equations •The rate at which the substance cools in air…

A: Let us denote the temperature of the air by Ta, the temperature of the substance at 100°C by t1, the…

Q: this is base on diffrenecial equation questions LINEAR EQUATIONS & EXACT EQUATIONS &…

A: The explanation of the given problem is below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Given L=3, k=0.4, the function f(x)=100-25x The heat equation is given by: ut=kuxx, x∈0,L, k≥0…

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

[ordinary differential equations topic]

Please solve the following problem

Provide a well-explained and understandable

step by step solution

Thank you

A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x =
3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 400 degrees Celsius. The ends of
the bar (x = 0 and x 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the
temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u- (2, 0.1).
Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

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

Topic: Exact Differential Equations Instructions: Solve the Exact Differential Equations. Kindly show the complete step-by-step solution, no shortcuts of solutions please. Note: I will rate you with “like/upvote” after if you show the complete step-by-step solution, if not then then i’ll rate you with unlike/downvote.” Thank you.
I attched formula for your refference. Please solve these sums according to this method. If you know this method then solve otherwize forward to others don't give wrong answer.
Diff equation question. Please solve step by step
Elementary Differential Equations (Upvote will be given. Please write the complete solutions legibly. No long explanation needed. Box the final answer.) Find the general solution. (4D3+4D2+D)y=0
5) [ordinary differential equations topic] Please solve the following problem Provide a well-explained and understandable step by step solution Thank you
this is base on diffrenecial equation questions LINEAR EQUATIONS & EXACT EQUATIONS & SOLUTIONS BY SUBSTITUTIONS please if you could answer faster i appreaciate of your effort
Higher order differential equation. Please show COMPLETE solution. Simplify and box final answer if possible. Please write legibly
SET J1 Differential Equations Note: If you have already answered the problems in this post, kindly ignore it. If not, then answer it. Thank you, Tutor! Content Covered: - Reduction of Order Directions: Answer the problem below by showing the complete solution. In return, I will give you a good rating. Thank you so much! Note: Please be careful with the calculations in the problem. Kindly double check the solution and answer if there is a deficiency. And also, box the final answer. Thank you so much!
Course: Differential Equations