Nindly answe is as soon as possibie. very urgent. ThankS (a) Solve it possible by method of separation of variable U = c²ug, u(0, t) = 0,u(1,t) = To, u(x,0) = p(x)

Q: an integrating factor for the DE dy+ydx=e3x dx is  1)ex 2)x2 3)y 4)x 5)ey

A: To find an integrating factor for the DE dy+ydx=e3x dx

Q: 4. If integration using u-substitution technique is used to solve for correct choice for u? (a) u =…

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Q: A cylinder object has radius 2 cm and height 3 cm. Use differentials to approximate the error…

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Q: Consider the IVP dy/dt = (2-t)/(y+2) where y(0)=1.  Find a formula for the solution. State the…

A: In this question, we find a formula for the solution. i.e. y(t) State the domain of the definition…

Q: Solve the given optimization problem by using substitution. Minimize S = xy+xz + yz subject to xyz =…

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Q: 3 Find the antiderivative of: a 6x²+4x by differentiating r3+x2 e3z+1 by differentiating e3+1 Va by…

A: Just differentiate the said term and then integrate both sides.

Q: Find dy and Ay for y = 3/x –1+ 2x at x = 2 with dr = Ar = 0.2.

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Q: b) Golve: 4x°y*+4x°4- sx y' + 24= 60x?+8x +1 on Co,00) (2) vsing the Method of Uaniation of…

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Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: Sx + 2y = 0 xy = -2 (x, y) = ( (smaller x-value) (x, y) = (larger x-value)

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Q: 2ydx + x(2 + x²y) dy = 0 %3D

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Q: The integrating factor of the given DE are already given below. What is the value of “n”…

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Q: y4) + 2y" + y = 0

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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: Two identical very long rods are at different temperatures T| and T2. At time t = 0[ they are…

A: Given data:  T1 and T2are different temperature  ut-k2uxx=0, -∞<x<∞, t>0 ux,0=T1,if…

Q: Use Euler's method to estimate y(0.02) ey-x y' 1 + e²y ,y(0) = 4

A: Given differential equation is y'=ey-x1+e2y with the initial condition  y0=4 and step size is…

Q: Use the method of Green's functions to solve the boundary value problem y" = -x?, y(0) + y'(0) = 4,…

A: The initial differential equation given is as follows: y''=-x2,  y0+y'0=4, y'1=2 Integrate both…

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: · Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x 0 to…

A: The given differential equation is,  dydx=y'=-3y+2e-x with an initial condition y0=2.  For…

Q: 0.4 at r 3, use linear approximation to estimate Ay Let y = 4x² + 6x + 2. If Ax |3| Ay =

A: Given y=4x^2+6x+2

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: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

Q: Find y asa x if finction of x2y"-7xy'+lby=0 to +16 where, yC1) =-2 and y'1D=3 00 3D

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Q: Solve the given optimization problem by using substitution. Minimize S- xy + xz + yz subject to xyz…

A: S=xy+xz+yz  =xyzz+xyzy+xyzx

Q: Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x = 0 to…

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Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: Solve for the general solution/particular solutio of the given using Bernoulli's Equation xydx + (x²…

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Q: 17. Using Runge-Kutta method of fourth order, solve dy y2-x2 dx y2 + x2 | with y(0) = 1, at x = 02…

A: Numerical methods: Ruge-kutta method

Q: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan…

A: This question is related to differential equation.

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

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Q: Reverse the order of integration 3 Lütfen birini seçin: a. 1 √3 √316 b. 1 So C. e d. 2 e. √3x 2² v²…

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Q: 2. Given y' = x² + y . With y=-1 when x=0. %3D Calculate y(0.4) and y(0.6) using modified Euler…

A: The given problem is to find the values of y(0.4) and y(0.6) using modified Euler's method for given…

Q: Q2 (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path…

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Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: Use Euler's method to estimate y(8) to estimate the solution to y' = y – 2x, y (0) = 1 %3D Use n = 4…

A: Given differential equation is y'=y-2x, y(0)=1.

Q: 4. x(x² – y² – x)dx – y(x² – y²)dy = 0, y(2) = 0

A: For the solution follow the next step.

Q: olve for the general solution of the given DE by using the integrating (x³ + xy2 + y)dx + (y3 + x²y…

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Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

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Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: Use Euler's method with step size h = 0.2 to approximate the solution to the initial value probler…

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Q: Consider xy' = y(lnx - In y) with y(1) = 4. Using Runge-Kutta method with h-0.1, approximate y…

A: Given,xy'=y(lnx-lny) y(1)=4; h=0.1To find: y'(1.3) using Runge-Kutta method

Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

A: In order to find the value of 'n', follow the following steps.

Q: use euler's numerical method to obtain an approximation of y (0.6) with h = 0.1 where y(0.2)=1

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Q: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

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