ди Q6/Determine the solution of u = 40 subject to boundary conditions u (0, t) = 0, u Ət (L. t)=0 and the initial condition u(x,0) = x+3, where L is the length of the bar.

Q: Find order and degree of y'+ (y")? =(x+y")? O a. 2,1 O b. 1,2 О с. 1,1 O d. 2 ,2

A: The given differential equation is                                              y'+(y'')2=(x+y'')2…

Q: Discuss maximum or minimum value of f(x,y) = y² + 4xy + 3x? + x'. 1) minįmum at (0,0) 2) maximum at…

A: Given that fx, y=y2+4xy+3x2+x3 Find: p=∂∂xfx, yp=∂∂xy2+4xy+3x2+x3p=4y+6x+3x2   q=∂∂yfx,…

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: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

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Q: x3 dx (x – 1)5 y = Select one:

A: First evaluate the integral by substitute method. Then apply the limits of integral.

Q: 9 = {(2, y) | 1< * < 2, æ² < y < 4}: If I = D then: / 12 + y) da dy =

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Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: Solve in variation of parameters y´´ + y =cscx

A: Given differential equation is: Solution of differential equation is sum of complementary function…

Q: 2 4 Ayz x = By + Cz' ||

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Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: Suppose that u = ry while r(s, t) = 1+ e3x²1 and y(s,t) = cos(ts) + 26. %3D du Make a dependency…

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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: Determine the interval where b must belong so that the function f(x,y)=x^(2)+bxy+y^(2)−b^(2)x−2by…

A: We are given, f(x,y)=x2+bxy+y2-b2y-2by..............(1) and x2+y2&lt;925................(2) We need…

Q: 3 If z= then: (2x² + y² )² ' dz az + y- -4z he dz dz + y- 4% az dz + x- y- = 4z az az = -4z

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Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: b. -2åx + 3d, - åz 2. If E = -xả, + yåy V/m, find the work involved in moving a unit positive charge…

A: We can solve using given information and calculate the work done

Q: 3. y" = Vx3 4. у" + 16у %3Dsec(4x) — 3

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Q: ди ди + x - Əx %| ду 0 =

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Q: use Lagrarge mul tipliers Sublect to the Constcair t to mekim,ze x+2y=5

A: Consider the given information. fx,y=x+4xy+6y and x+2y=5 Now, make the auxiliary function.…

Q: 2 32. The equation of the straight line that corresponds to the null-space of A = -5 is: -4 10 2 (A)…

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Q: Determine the maximum r-values of r-7cos4e. 8- 0. * 3x 3x e= 0, e= 0, .

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Q: The line y 을 16 has x-intercept 3. -8)-and is perpendieular to Ahe line Passes through (4,pand…

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Q: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

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Q: An equation of the straight line normal to surface x2 - y3 + z = 8 at the point P(2, -1, 3) on the…

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Q: Find equations of the tangent plane and normal line to the surface x = 5y² + 5z² — 28 at the point…

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Q: d²y 1. + k?y = 0. dx2 2. at2 3. (x? + у?)dx + 2xydy %3D 0. 4. y' + P(x)у %3 Q (x). 5. y" — Зу' + 2у…

A: Use property of linear and non linear equation

Q: 2. The wave heights h in the open sea depend on the speed v of the wind and the length of time t…

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Q: Q2/A/<he di fferential equation is yedx +3xay+dx +dyno diff erential when fineling the solution to a…

A: To find: The solution of differential equation y2dx+3x2y2dx+dy=0 and also find the constant (c) at a…

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: Find an equation for the tangent line to the graph of f(x) = -2x2 + 2x + 3 at the point where x = 1…

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Q: At what interval is y=2x4- 4x2 concave downward? Ux> 3 3 3 3 V3 3 <x< 3 3 <x< V

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Q: e of y = -3 sin x + 5? (I Vミー

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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