Find temperature in a rod with length L=2 and: Ut = 4uxx u(0,t) = 1,u(2, t) = 3 0 < x <1 u(x,0) = f(x) ={x- 2 1

Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

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Q: equilibrium

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Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 4xyz + 7yz2 s(x,…

A: As we know that the sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 Given:…

Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0 Have to be convert to exact by integration method

A: Given  Differntial equation (2xy ln y)dx+(x2+y2√y2+1)dy=0

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Find a function w = ƒ(x, y) whose first partial derivatives are ∂w/∂x = 1 + ex cos y and ∂w/∂y = 2y…

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Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

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Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

A: Given

Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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Q: Find a set of solution. Integrating factors found by inspection.   y(x2 + xy2 - 1) dx + x (x2 + y2…

A: Given the differential equation y(x2 + xy2 - 1) dx + x (x2 + y2 +1) dy =0. We need to find the set…

Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: The maximum rate of change of the finction f(x, y, z) =x In(yz) at (1;2;5 is equal to: O None of…

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx - (x +…

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Q: What is the integrating factor of y (x² + y) dx + x (x2 - 2y) dy = 0? -1

A: We will find out the required integrating factor.

Q: ou must show ALL of your work. 2) Solve the Boundary Value Problem.   y"+9y=0,   y(0)=1, y'(pi)=1

A: Given:  y''+9y=0 is second order differential equation Differential equation D2+9=0 Auxilary…

Q: Let 2x2+ 3x+Y a) Find the differential dy when x = 1 and dx=0.1 %3D b) Find the difiea ial dy when…

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Q: Find the first partial derivatives with respect to x, y, and z. Ex, y, 2) = 3x?y - 6xyz + Byz? ,(X,…

A: We have to solve this problem by partial derivative method.

Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y. How is dV/dt…

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Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: Solve for the general solution of the given DE by using the integrating factors found by inspection.…

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Q: xy' + y = sin(x), y(3) = 0, y'(3) = 0. Yh = C1x + c2x ln(x).

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Q: Eliminate the arbritrary constant/s. Show full solution. x= -In t, y= at + bt?

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Q: y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 5xy'. Determine…

A: Given differential equation, 5xdydx=x-y,  x=3,y=6 dydx=x-y5x put, y=vx dydx=v+xdvdx now put values…

Q: Evaluate the deflection of a vibrating string of unit length having fixed ends with initial velocity…

A: Consider the wave equation    ∂^2u∂x2=1c2∂^2u∂t2     .....(1)   here U(x ,t) is the defection of the…

Q: find the general solution using integrating factor method  dy/dy - y/2 = 2sin(3t

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Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: (tiy t 3y" -x)dn + x (x+ Jdy = 0 2

A: Given differential equation is  4xy+3y2-xdx+xx+2ydy=0 find the general solution of the given DE

Q: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx – (x +…

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Q: Find the indicated partial derivatives. TC f(x, y, z) = v sin²(x) + sin2(y) + sin2(z); f0, 0,

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Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

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Q: Find the general and particular solution that satisfy boundary condition • Boundary Condition 1. y =…

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining question…

Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: • Find the general and particular solution that satisfy boundary condition • Boundary Condition 1. y…

A: We have to use y=vx and dy=vdx+xdv

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: Find the general solution using Integrating Factors Found by Inspection y(x^2 y^2 – 1)dx+ x(x^2 y^2…

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Q: Use Euler's method to numerically integrate dy -2x3 + 12x2 – 20x + 8.5 %3D dx from x = 0 to x = 0.5…

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Q: Find the total differential. z = 6x *y5 iz

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: What is the integrating factor of 2ydx + x (x² ln y – 1) dy = 0 ? Oy O y?

A: Question is solved.