The solution of Laplace equation :0, where 0 < x < 6 and dy? 0

Q: Suppose that y= 2(1- e *). Compute y' and show that y' =2-y. y' =] 2-y%3D Does y' = 2-y? O Yes O No

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Q: Solve 1) y" + y = e* + x² 2) y" – y' – 6y = e-2x + 4sinx

A: here first take d/dx = D then make its auxilary equation then find complementary solution then find…

Q: 3.4 Compute the angle between -- ). --- 1 y = 2 using a. (x, y) := x'y TBy, 2 В:- 1 b. (x, y) := x 3

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Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: Choose the correct answer     If A = {x: 0 <x <2} and B = {y: O <y <1/2) Find C = AU B and D = A…

A: Provided information is ; A = {x: 0 &lt;x &lt;2} and B = {y: 0 &lt;y &lt;1/2) we know that ; AUB =…

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: Determine the interval I for which the following DEQS have a unique solution whose graph passes…

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Q: 12.) Let h: IR³ -> IR5 and g: IR² -> IR³ be IR² -> IR³ be given by hcxy. 2) - (xyz, ex* x sin(y),…

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Q: Previous 8) Find y' if y = (2x - 1)(x + 1). %3D a) O 4x + 1 b) O -4x + 1 c) O 4x - 1 d) O -4x - 1

A: We have to find derivative

Q: Solve the Followings : 1. dy (x + 4)

A: Given: dydx=(x-y)2Solution:dydx=(x+y)2⇒dydx=x2+2xy+y2Now separating x and y terms, we get-y2…

Q: 7. Integrate. So So (x-1)² x² + y2 dydx

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Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: rks) Find the solution of the following problem: Utt = 9uzz, x > 0, u(x, 0) = x², u(x, 0) = 6x +3,…

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Q: 1. Disk Method a. y = x2,x = 0, x = 2, y = 0, about the x ахis а.

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Q: Find the maximum and minimum values of the ratio x’A x/x'x for any nonzero vectors x' = [x1, x2, X3)…

A: We have to find maximum and minimum value of ratio x'Ax/x'x

Q: Find the solution of the following problem: Uu = Uga I> 0, t>0, u(x, 0) = 2 u(0, t) = 0, t2 0. - z,…

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: Find the equation of the tangent plane to f(x, y)= x´ – x y – y at point P (1, 1, -1).

A: Consider the equation

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.