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 is given by the function f(x) = 100 - 25x 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 us (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

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

A:

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: 7 solve the differensial equation. (2x +31) dx + (y x ) d y =0

A: Given differential equation is:(2x+3y)dx+(y-x)dy=0

Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: dy VI+x = y° (y + x) (Bernoulli) dx,

A:

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

A:

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: 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:

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

A:

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: Write the differential equation and then determine whether you have overdamped,critically damped,or…

A: Introduction: The differential equation of motion of an unforced damped harmonic oscillation is…

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:

Q: For the differential equations below, write in standard form, and name the type of equation. Then…

A: Here we will estimate the required form.

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: y a X1 b a11x + a12y = b₁ a21x + a22y = b₂ X ✓ Choose... Ordinary differential equation(s) Curve…

A:

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.