Solve the following heat equation = ut (x, t) u(0, t) = t, u(1,t) = 0, u(x,0) = x². Uxx (x, t) + x sin(t),

Q: Find dy 2 2.

A: From the given problem:   x2y2=x2+y2   As we know that the Power law:   dxndx=nxn-1   Now…

Q: If A = A−¹ . 9 7 1 0 1 5 00 01

A: The matrix is given byTo determine: The inverse of the given matrix.Formula used:

Q: 2 -1 se s? +4 .2

A: Given:       L-1se-π2ss2+4 Apply inverse transform rule:       if L-1Fs=ft then L-1e-asFs=Ht-aft-a…

Q: Simplify. 10m n² 5mn4

A: To simplify the below expression.

Q: S t Vat²-b dt

A:

Q: 10. 2 w² + 4w W 1 dw

A: Given problem:-

Q: Solution for h?

A:

Q: 7. Let ƒ(x) = 4x − 3, g(x) = x² + 4, h(x) = x + 5. Evaluate the following.

A: Given f(x) = 4x - 3 g( x ) = x2 + 4 h( x ) = x + 5

Q: 2.25x.2

A:

Q: What is AA-. wbetce 2 2 1 2 2 2 1 1 A = 2

A: To Determine: find AA-1 Given: we have a matrix A=122212221 Explanation: we have a matrix…

Q: 1. a 2 b 4

A:

Q: 3) %3D 2.

A: Two dimensional wave equation , by using separation of method

Q: 4. w/- 4. 2.

A: Given:

Q: 52 +9

A: Given,  is the inverse Laplace equation. We have to find the solution as follows:

Q: A = 1 1 0 0 1 -1

A: Note the following fact :

Q: 0.4r-0.13-0.7r=3r-5.74

A:

Q: Evaluate. .3 S (-x² + 4x – 5)dx -2

A:

Q: / esx+3 dx = %3D

A: To evaluate the integral :- I = ∫e5x+3 dx Substitute    u = 5x+3du = 5 dxdx = du5

Q: Multiply. (ex − e−x)2

A: Here we multiply this:

Q: Solve for x. 3 11 2

A: Consider the following figure. In above figure AB+BC⋅BC=CD+DE⋅CD.....1

Q: Write a triple integral which computes the integral of the function f(x,y,z) = xz over the region R…

A:

Q: Solve for x. 11 2

A: The value of x is, 19 The detailed solution is as follows below:

Q: Solving a System of Linear

A:

Q: (x, 5), (2, 6) m = 3/4

A: Let the equation of line be y=mx + b  ...(i) We have m=3/4 = 0.75

Q: Given: AB = AC; OB = 0C a. Is it possible to prove that ZAOB = LAOC? b. Is it possible to prove that…

A: Definition used-               SSS congruence -                If three corresponding…

Q: 3. e2In 2x %3D 4x. B 2r. 4x D In 2x.

A:

Q: .2 y = 4 - x² and x +y = 2.

A:

Q: Simplify. -16 6. 36 4 i 2 3 -4 4

A:

Q: Simplify. 7/16-V54

A:

Q: 4. %3D х+2 х-5 :- 3.

A:

Q: To-22 (1ny-8x) dy da

A:

Q: W X Y Exs. 4, 5

A: Given: mXW⏜=60, mWZ⏜=70, and mZY⏜=70.

Q: Steť?+1 dt

A: Let take t^2 = z  Then.differentiate it ansd solve it as. Below

Q: (a +3)2 = 25 %3D

A:

Q: 0.3)1536.

A: 0.31536 Note: Multiple questions are given, we are answered with first question only.

Q: bim nto

A: when we get 0/0 form, libnitz rule is used.