Solve the problem: Ut - 2 Uxx u (x, 0) u (0, t) = = h, = x, sint, t> 0, 0 < x < 1, 0 ≤ x ≤ 1, ur (1, t) +u (1, t) = 2, h = constant, t≥ 0.

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: TRANSCRIBE THE FOLLOWING SOLUTION IN DIGITAL FORMAT

A: Want: To transcribe the given text in digital format

Q: Solve 2x y da + (x+3y*)dy = 0 Ax'y + xy* = € |9 r*y+y* = c

A: 2x y dx + (x^2 + 3y^2) dy   Here we have to solve the given differential equation:   The given ODE…

Q: Solve Fyy + 3 Fxy + 2 Fxx 3D х, F (х, 0) 3D —2 х,д, F(х,0) — 0. ху XX F(x, y) =

A: To solve the below partial differential equation. Fyy+3Fxy+2Fxx=x,  Fx,0=−2x, ∂yFx,0=0

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

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Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

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Q: Find a function that satisfies the conditions f " (x)=x8, f'(0) = 13, f(0) = 10.

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Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

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Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

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Q: Find nd cos(z ² + y²)dA where D = {(x, y) | 16 ≤ x² + y² ≤ 81} D

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

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Q: x3y+2x²y" + 4xy' - 4y=0 Assume the values of x are (0, 0)

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Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: Find a solution of x dy = y²-y that passes through the indicated points. dx (a) (0, 1) y = (b) y = 1…

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Q: 1. Given f(x, y) = x' + y* find and ax?' dy' axðy дудх 2. Find whether the function F = (r² – y' )i…

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Q: What is the minimum value of y = 3 + cos 2x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=&lt;t sin t+cos t,2t2,sin t -t cos y&gt; Then vector is given by r→t=t sin t+cos…

Q: Solve the IVP: X' = AX, where -4 1 1 A 2 -5 0 -4 1

A: Given I.V.P. is  ,             X'  =  AX  where ,…

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: 7. Let T: R4 → R4 be a linear transformation whose standard matrix is 7 4 10 6. 16 -4 12 12 -8 -6 -2…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

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Q: Solve vxx + vyу %3D ху ,х € (0, п), у € (0, п ) v(0, y) = 0 v(п, у) %3 sin2y vх, 0) — sin3x v(x, 7)…

A: Given: vxx+vyy=xy   …1, x∈0,π, y∈0,πv0,y=0vπ,y=sin2yvx,0=sin3xvx,π=0 We have to solve equation (1).…

Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

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Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

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Q: xye-(2²+v°+z*). Find all points (x, y, z) such that Vf(x,y, z) : Question 2. Consider the function…

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Q: ƒ(x) = x² − 4x³

A: Inflection point: A point where the real valued function has neither maxima nor minimais called the…

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A: Given: The equation is ∂2z∂x2+∂2z∂y2=e-xcosy. Also, the given equation tends to 0 as x→0 and its…

Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

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Q: Use Midpoint Rule, the distance travelled during this period is, M, =| v(x, )+ v(x, )+ v(x, ) + v(x,…

A: Definition used – The value of the function at a point – The value of the function at a point can…