Determine u(x,t) for the problem below: a?u a2u 25- (0 0 at2 u(0, t) = u(16, t) = 0, t>0 u(x, 0) = 0, du(x, 0) %3D %3D (0

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Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: s2, y'(0) = 0 where/burada h(t) to, 0 <t<1 y" – 2y' + y = h(t), y(0) = 0, %3D %3D t21

A: we have giveny"-2y+y=h(t)   y(0)=0  y'(0)=0where h(t)=2  0&lt;t&lt;10       t≥1first find…

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Q: а. y' +y tanx %3D sесх + сosx b. 1 -/dx+x?dy)=0 (x² - y?) C. yy' – 2y? = e* С. d. 1 -(хdy - ydx)3D0…

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Q: dw Use an appropriate form of the chain rule to find dt = In(10x² – 2y + l2³); x = tỉ, y = tỉ, z =t?…

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1)=Q %3D

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Q: 2s – 5t & y = 6s – 8t. %3D Let z(x, y) = x + 9y? where x = az дх ду да dy dz Calculate ds & and…

A: We use the chain rule

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Q: d²y 1 dy y + y(3) = 0.009u, y(10) = 0.003s - dt2 t dt Use an appropriate method to find y(t).

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Q: S f(x) dx = 5 ve 8(y) dy = 7 olsun. R = [0,2] × [2,3] olacak şekilde %3D %3D I = SSrf(x)g(y) dA…

A: To find the solution of double integral.

Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

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Q: Let y' - 2y = 0, show that: i) y= e2x is a particular/exact solution %3D %3D %3De

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Q: C is given by x = t°, y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + x dy + y dz)

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Q: dz Use an appropriate form of the chain rule to find dt z = 6x°y3; x = t8, y = t 52,3. %3D Enter the…

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Q: Use the Chain Rule to find dz/dt. z - x2 + y2 + xy, x = sin(t), y - 2e Use the Chain Rule to find…

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Q: The solution of ë+w?x = fsin wt with initial conditions r(0) = 0 y a(0) = 0 is given by %3D %3D

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Q: af du (a) f(x, y) = sin-¹ (b) f(x, y): = x+y (c) f(x, y) = In ( t = 1 and u = 2 af and where Ət 2.…

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Q: dy dx Assume x and y are functions of t. Evaluate for 4xy - 2x + 4y³ = - 28, with the conditions dt…

A: Given,            4xy - 2x + 4y3 = -28 and dxdt= -16, x = 4, y = -1

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Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: Consider the IVP: y= 3z – 4y-2, y(2) = 3. A) Use Euler's method to obtain an approximation of y(2.4)…

A: The given differential is y'=3x-4y-2  , y2=3 we know the Eular method is yn+1=yn+hfxn,yn

Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: y' = 2y t y (1)=1 and and abtain y, Y₂ y h =…

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Q: Q.2 Evaluate () dx. 2x (i) Using Trapezoidal rule by takingh = 0.2, h = 0.5 & h = 0.25. %3D %3D %3D…

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Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: Integrate f(x,y)=x²-7y over the curve C: x² + y² = 64 in the first quadrant from (0,8) to (√32.√32)…

A: Draw the given equation of the curve x2+y2=64 and the given points. The given curve is between…

Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: 3. Given: y = f (u) and u = g(x), find dy/dx: a) у%3D сos u, и%3D—х/3 b) y = tan u, u = 10x – 5 - с)…

A: Our aim is to find the derivative of the above expressions.

Q: 4. Transform the equation y'= f(x)dx+ f(y)dy = 0. 2xy Into the form of varlable separable…

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Q: dy dx Assume x and y are functions of t. Evaluate for 4xy - 7x+4y3 = - 92, with the conditions dt =…

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Q: c) W (f(x), g(x), h(x)) = 0 Q2) L-1 a)-2coshnt b)-2sinhnt c)-2cosnt d)-2sinnt Integrating factor…

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Q: dz Use an appropriate form of the chain rule to find dt z = 6x°yl0; x = t³, y = t³ 10. Enter the…

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Q: x + 2y + 3z = 0 Find the solution r = (x, y, z) to 3x + 2y + z = t as a function of t. 2х - у — z…

A: NOTE: d) should be dr/dt  not dr/dx  .

Q: If f (x, y) = 4e4*cos (y - 1) , then the linear approximation at (0, 1) is %3D (A) 4+ 16x (B) 4+4x…

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Q: y(y+2x - 2) dax – 2 (x +y) dy = 0

A: We have to solve the given non-exact and first-order linear differentiable equation…

Q: at at 4) Let t = ,u = x² – y² ,v = 4xy³. Find· ay əx

A: To find: The value of ∂t∂x, ∂t∂y. Given information: t=uv, u=x2-y2 and v=4xy3 Concept used: Quotient…

Q: ürkçe: f(x, y) = 4 + x° + y° – 9xy fonksiyonunun yerel ninimum değerini bulunuz.

A: Please refer to the image below

Q: • Consider the 2nd order homogeneous linear diff eq: * + 2 – 3y = 0 a) Which functions below satisfy…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Applying variation of parameters to the DE: " – y = et + e-*, we get the following system of…

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Q: Q1) Evaluate SSS, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 < y < 1, 0 < z < x + y }.

A: Since you have asked multiple questions, we solve first question for you. For other question to be…

Q: Solve simultaneously x' (t) – y (t) + z' (t) = 1 - æ (t) + y' (t) + z (t) = 1 - 1 a' (t) + y' (t) –…

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Q: dy f(x.y), y(x,)=y, by Euler's method is dx The third approximate solution of

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Q: dx 8y – x² – 12 dt - | dy - 2(x – 2)(y – 6) dt (a) Does there exist a yo > 0 such that if x(0) > 0…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Let y(x) be the solution of y' = y − 4x such that y(1) = 1. Using a step size of 0.5, set y0 =…

A: I am attaching a picture where you will get step by step solution first I write the formula of euler…