10 Consider the heat equation in one spatial dimension: U - Uzz = 0, IER',t> 0. Let u(z, t) = v(£) = v(r - t). What is the equation for v(E)? Find the general solution for v(£).

Q: 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) - v sin(e) and yusin(0) + v…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: b) This is a velocity-time graph of a particle. The area of the left shaded region is 6. The area of…

A: Since you have posted multiple questions, as per our company guidelines we will solve only the first…

Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: Use the Chain Rule to find dw/dt. dw dt = w = In x² + y² + z², x = 3 sint, y = 8 cost, z = 6 tan t

A: So, After the differentiation the final answer for the question is:…

Q: w = xy, x = e", Given Find dw/dt

A:

Q: 5. Let f(x, y) = x+4 cos y. (a) Evaluate f (0, z/3), f.(0, z /3) and f,(0, x/3). (b) Use the results…

A:

Q: Evaluate S(ti + tj + t°k)dt = i+ j+ k.

A:

Q: Find the chiftes ki,ke, ks) = then

A: The given question belonging to the calculus in which we have to find the total derivative of the…

Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

A:

Q: 4t-5 b) Find for y = sinvt – 1, and x = dx cost b) Find dx for sin?x – cos?y = tanx Jz dt %3D t+2

A: We have to find dydx (1) y=sint-1 and x=4t-5cost (2) sin2x-cos2y=∫ytanx31t+2dt

Q: z= f(x,y) ; x= r-s1 , y= r2s and zx(0,-1) = -24 ; If zx(0,-1)=-18, what is the value of the…

A: Given that z=f(x,y),     zx(0,-1)=-24 and  zy(0,-1)=-18x=r-s and y=r2s We have to find zr(0,-1).

Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

A:

Q: The internal energy U of a gas can be expressed in the form U=f(p,V,T) with variables defined by: p…

A: Step 1:Use Ideal gas Law;PV=nRTInternal energy can be related to ideal gas…

Q: Use the differential dz to approximate the change in the function z (shown in the image) as (x, y)…

A: Given that:   The given function z = f (x, y) moves from the point (1, 1) to the point (1.03, 0.95),…

Q: when u = 0, v =1 if du Use Chain Rule to find z = sin ry + x sin y, r= u² + v² and y= uv.

A: Given: z=sinxy+xsiny, x=u2+v2 and y=uv. To find: ∂z∂u at u=0, v=1. Solution: Partial derivative of a…

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: (a) Let f(x,y) = x² – 5xy. (i) Find the directional derivative at (2, 1) in the direction of i = -i…

A:

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: 11) Calculate the Jacobian, J, for the change of variables x = u cos(e) - v sin(e) and y = u sin(0)…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: Estimate the amount of change in f (x, y,z)= cos (7xy)+xz² if the point P(x,y,z) moves a distance of…

A: Given that f(x,y,z) = cos(πxy) + xz2 If the point (x,y,z) moves a distance of ds=0.1units from…

Q: Consider the function f(x, y, z) = 3x2 cos(y) + e 25. Calculate grad f at the point (2,0,1).

A: The gradient of a function, often denoted as grad or ∇f, is a vector that points in the direction of…

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.