d’u = 0 at x = L. Find the conditions u(0) = 0, dx 2 approximate solution by using weighted residual method.

Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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Q: Find the solution for following variable separable equation: x² (dx/dy) = y - xy , y(1)=1

A: The main objective is to solve the given variable separable equation.

Q: c. y = V6x2 +1 с. Rewrite y = y'=

A: we solve this differentiation by using chain rule

Q: Find the linear approximation to f(x)=x2+1x−2 near a=3.

A: Given: f(x) = x2 +1x − 2; a = 3

Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Find a general solution of y'" = (- 50 – 50 i /3) y. ... y(x) = C, e +c2 e-

A: The given differential equation is y''=-50-50i3y Demoiver's theorem for fractional power  If rcos…

Q: - y" 3y'+2y=- 1+ e-x Use Variation of Parameters. Do not simplify final result.

A: Step 1: Step 2: Step 3: Step 4:

Q: (15) y "'+ y " =e (16) y () – y (4) = 1 %3D

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Q: Solve dy/dx = y -x with y(0) =1 using the linear multi-step method Yi+1 +(3/2)yı -3yı-1 +(1/2)yi-2 =…

A: First solve the given differential equation: Given : y'=y-xy'-y=-x The given differential equation…

Q: x²y" +xy' – y = T

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Q: • ex+y -2y-2=Ce e2x+y +2y-2%3DCEY e2xy -2y+23DCEY

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Q: Verify that y = c is (1+ce') (1– ce') is a solution to y' = + (v² – 1) , where some constant.

A: For verifying given thing, we find solution of given differential equation Now, for finding solution…

Q: f(7,y) = 8z² + 5y² + 4z'y+e7=y %3D Calculate 710

A: The given function is

Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties when…

A: We need to Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties…

Q: y = xy' – y* + 1 find general solution and particular solution.

A: Given, We have to find general and particular solution for it. Working:

Q: Find the general solution of the equation by the variation of parameters method: y" – 2y'+ y = æ 2e"

A: We use the procedure of method of variation of parameters.

Q: d’y - 2 y = 5x' + In(x²). dx

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Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: Approximate y(0.8) in the function y' = x - 2y when y(0) = 0, x(0) = 0 and the stepsize is 0.2 using…

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Q: Q6/Use Runge-Kutta method to solve (dy/dx = x³ + y2), y(0) = land h= 0.2, find y(1)

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Q: y' = 2x - 3y + 1, y(1) = 5; y(1.5)

A: y'=2x-3y+1, y1=5, h=0.1. We have to find y1.5.

Q: An airline claims at the Average number of years of experience of its pilots is 18.3 years. In a…

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Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: Similarly, dx/dz can be obtained from a linear regression of x on z x = ax + ß₂z+ ε with the OLS…

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