Find the approximate solution of the equation Uxx = 4u; by Crank- Nicolson method subject to u(x, 0) = 0, iɖ0, t) = 0 and u(2, t) =2t for three-time steps given that Ax= Ay= 0.25.

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

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

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Q: Find the x-value where the relative maximum of y=ex4−x2y=ex4-x2 closest to x=0x=0 occurs. When you…

A: Given, y = ex4-x2 First  guess x = 0   We have to find the second guess using newton`s method.

Q: Find the general solution of the following DE in explicit form. y' =2+2/y-2x+11

A: Solution: The differential equation is y'=2+2y-2x+11 Suppose that v=-2x+y so that y=v+2x Then,…

Q: e the following nth-order equation using the variation of parameter method: y"-3y"+3y'-y=

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Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

Q: Solve the following PDES by separation of variable metho (i): u +U, = 0 (ii): y'u, –x’u, = ди (iil)…

A: (i) uxx+uyy=0   ...i solve the PDE using separation  of varaible let u=XxYy differentiate with…

Q: (d) Find M' (e) Find a particular solution to Ÿ = AỶ and write out the general solution.

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Q: b) Use method of variation of parameters to find the general solution to the equation x²y" – 3xy' +…

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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: Use the method of variation of parameters to determine a particular solution to the given equation.…

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Q: find the length of y=√x² from to += 12 x = formula 3 L = So 9 Ht( f (x) J² dx

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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: Solve using the method of variation of parameters: y" + 4y = sec X. %3D

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Q: Find the general solution of the equation y" – 2y' + 5y F0 Do not need to show your work, just give…

A: First we find the auxiliary equation and then we find the general solution of the given homogeneous…

Q: 6. Use variation of parameters to solve y" - 7y' + 12y = e²r. (10 pts.)

A: Solving the differential equation y′′−7y′+12y=e2x using the method of variation of parameters 1.…

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: Find the general solution of the equation y" – 2y' + y= 0 Do not need to słow your work, just give…

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Q: Use the variation of parameters to solve the given equation: (a) y"+y"-4y'-4y = 2e¯* +4e²x

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Q: Q3- Solve only one of the following: A- Find the approximate solution for the function y' x + y…

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Q: Q2) Solve (y+ysin x) dx - (cosx- 2xy +) dy = 0

A: Given differential equation is  y2+ysinxdx+-cosx+2xy-1y2+1dy=0 Comparing it with Mdx+Ndy=0, we get,…

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

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Q: The equation x - Rx¹ = 0 has x = R¹/2 for its solution. Establish Newton's iterative scheme, in…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) and the initial approximation of the…

Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67