: Solve by using Separation of variables method? E= k a²u for 0 < x < L, t > 0 u(0,t) = u(L,t) = 0 for t > 0, u(x,0) = x(L-x) for 0< x < L

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xydx - (x + 2)dy = 0

A: Given problem:- Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS.   xydx -…

Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)=0 Find y(0.1)?

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Q: For non-homogeneous equation y" – y' – 2y = x, %3D how to choose a particular solution of y, =? Do…

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Q: Exercise 5 Using the method of variation of parameters, the particular solution Yp for y" + 3y + 2y…

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Q: Q: Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z = 1 x- y+ 5z = -2 2x + y = 3

A: The given system of equation is  3x + 2y -z =1 x - y +5z =-2 2x +y =3

Q: Find the solution of y- dy --x = 0 using separable variable method. dx +C 2 3 Ob. None of these y +C…

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Q: • Determine the particular solution given the general solution y(x) = c,e3x + cze-* and the boundary…

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Q: Use Euler's method to approximate the solution to y' = y + 2t , y(-1) = -1 on the interval [-1, 1]…

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Q: (B) Find the solution of f(z) = x'+6x'y+i 3x'y by using Cauchy-Riemann method

A: we have to solve the given problem

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: and obtain y' = 29 t y (1) =1 y, y, and y. 3…

A: Hint: Formula for finding n-th approximate solution of IVP  dydx=f(x,y), y(x0)=y0  is…

Q: In each exercise, obtain the particular of solution. a. (y + Vx2 + y²) dx – x dy = 0; when x = V3, y…

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Q: Find a continous solution satisfying the equation and the initial condition (1+x²)y/ +2.ry = P(x) r,…

A: we have given a first order differential equation with piecewise function P(x) we need to find a…

Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²u"+xy' +(x² – !)u…

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Q: 2. y() + 2y" - 2 А. 1 В. 2х C. x? D. ½ x?

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Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

A: Given query is to find indicated derivative.

Q: Let y(x) be the solution of y' = y − 6x such that y(2) = 2. Using a step size of 0.5, set y0 =…

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Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: Solve the following equation by using separation variable method: y(x,0)=10 t> 0 y, (0,1) = y,(7,t)=…

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: Compute the solution of the IVP Sz(t) = (sin f)z(t) + sin t, l-(4) = 1, using the method for linear…

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Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: Use the finite-difference approach to solve y"=-2-(A+x<)y for boundaries y(-1)=0 and y(1)=0 with…

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Q: (x² + y²)dx – xy dy = 0

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Q: Q Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z 1 x- y+5z = -2 2x + y = 3

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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: Use the method of reduction of order to find a second solution to t’y'" + 2ty' – 2y = 0, t > 0 Given…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Use 4t order Runge-Kutta Method to solve dy = y' = x+y, y (0) = 1 & Y(2) = ? Use h = 0.5

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Q: Show that the equation x3 + y* xy? is both Bernoulli and homogeneous. Solve this equation using the…

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Q: (y+x*y²) dx +x dy = 0 5.

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Q: Using the Euler's method with step size h = 0.2, approximate y(0.4) if %3D y = y? – 2.2, y(0) = 1.

A: The solution is given by using the Euler's method as follows

Q: the general solution of yv1+x²dx + x/1+ y?dy = 0 using variable separable method. 3. Obtain X-

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Q: Use the separation of variables method to solve 4UTr H Utt: 00 uz (0, t) = uz (2, t) = 0 u(x,0) = x,…

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Q: Q4: Solve by using Separation of variables method? = 4 for 0 0 (0.e)=27.t) = 0 for t 20, u(x.0) =…

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Q: Use the method of separation of variables to solve: - = 0 in (0,1)×(0,+∞), at? ôx (1) u(0,t) = u(1,…

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Q: Determine the type of DE/method of solution to be used and solve. y(y3 − x)dx + x(y3 + x)dy = 0

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Q: it as a Bernoulm cquaion in the uependeht varlavic A. 0. 2x'y = y(y? + 3x). Solve by two methods.…

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Q: b. Solve by using variable separation method. = 0 ax2' ay2 Which satisfies the conditions, u(0, y) =…

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Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

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Q: Use the method of successive approximations to solve the I.V.P y' = y(1– 2x), y(0) =1.

A: Given The given I.V.P is y'=y1-2x,         y0=1. Apply Picard's formula or successive approximation…

Q: A. y" – 2y + 1 = (x + 1)e²x

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Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

A: We take y'=z the Given equation is y''=y+xz,y(0)=1,y'(0)=0,y(0.2)=?…

Q: (b) For the solution that satisfes v(0)1, sketch the solution curve and estmate the following v(0.5)…

A: (b) The solution that satisfies y(0) = 1 can be sketched as follows:

Q: Solve the equation (y+ u)Ux+yuy = x -y with the initial conditions u(x, 1) = 1+ x. %3D

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Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Solve an IVP:  y'' − y = g(t); y(0) = 0, y'(0) = 2, where g(t)= 1, tt

A: When t&lt;2 then the solution:   y=32et-12e-t-1 When 2&gt;t then the solution:  y=32et-32e-t-t

Q: The function U(x, y) satisfies the equation a²U_a?U + ax2 ' ay2 = -2, at every point inside the…

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Q: Q3/ Determine the solution of a?u du arz subject to boundary conditions u(0,t)= u(2,t) = 0 %3D at…

A: Given pde is heat equation. Solution of this pde given by

Q: 9. Find the general solution of (D² +µ)y = 0, satisfying the boundary conditions y(0) = b and y(L) =…

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Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: From the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2,  y' = 2, obtain the value…

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