(2х — Зу)dx + (2у - 3х)dy %3D0

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: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

A: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

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

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Q: Determine if the equation (dfferential form) is exact and find the solution if it is…

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Q: Obtain a family of solutions using the indicated process. For those items with initial values,…

A: solve using substitution  2x-y+1dx-y-2xdy=0 with initial condition y1=2

Q: y(4) + 3y" + 2y = 0

A: We have to solve given differential equation.

Q: y" + y = 2x

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

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Q: dy-Hy-5 te %3D xp

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Q: 4. (D² + 2D + 5)y = 4e-*cos²x

A: Given differential equation is: d2ydx2+2dydx+5y=4e-xcos2x Auxiliary equation corresponding to given…

Q: Identify if its:       a. Homogeneous DE,       b. Exact DE,       c. Linear DE of order one and…

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Q: 4. Solve the DE, = ! + 2(4), using the homogeneous method.

A: Given, dy/dx = y/x +2(y/x)3/2        .............(1) Assuming  y = vx Differenetiating y with…

Q: (Dª + D² + 10D)y= 0 , y(0) = 0, y'(0) = 6, y" (0) = 4, y"(0) = 4

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Q: 1. y" + 4y'+ 3y = 12 В. 12 А. 4 С. -4 D. 4x

A: Given y''+4y'+3y=12(D2+4D+3)Y=12Auxillary equation is m2+4m+3=0Upon solving, m=-1,-3CF,…

Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: Find solutions using Exact Equations 5. Solve (2t3 + 3y)dt + (3t + y – 1)dy = 0

A: Firstly Compare given differential equation with Mdt+Ndy then find the exactness of equation and…

Q: Solve using Gaussian method x-y+4z=10 3x+z=3 x+4y+z=11

A: Given:

Q: By using linear method, solve dy %3D

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Q: Solve numerically Au = 0, u(0, y) = 70, u(3, y) = 0, u(х, 0) 3D 10, и(х, 3) —D 90, 0<х <3 0 < x <…

A: Given that: ∆u=0,…

Q: Use Cauchy-Euler equations solution method to solve b. x²y" – 5xy' + 8y = 4x6 s.t y(1) = 0,y'(1) = 0…

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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: Solve for the orthogonal traectories y2= 4x²(1- kx) %3D

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Q: 4. Solve eu, - uu, = 0, u(0, y) = -y %3D for small |r.

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

A: We have to find the solution of the given problem.

Q: y" + y" = 3

A: Solving the given third order differential equation

Q: a) (x² + y² + z²)² = xyz %3D

A: see the attachments below

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: Use Newton-Raphson method to solve the system x* + y – 1 = 0 y* – x +1 = 0 with the starting value…

A: We will use the following Newton-Rapson formula for finding the roots of 2 variable equations.…

Q: Find the root of system of equations using Newton Method . Employ initial guesses of x=y=1.2 y=-x²…

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Q: Solve the equation ru, + (x + y)uy = 1 %3D on dof:

A: In this question, we solve the partial differential equation by using characteristic method.

Q: 6. y" – 2y' = e* A. 2e В. -2е C. e D. -e

A: Given that the non-homogeneous differential equation is       y'' - 2y' = ex

Q: y" + 2y' = 2te

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Q: 5. y" = 4 А. X В. 2х? C. ½ x? D. x'/3

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Q: Transfer the Cauchy-Euler equation to a constant coefficient equation and find the general solution;…

A: We have to transfer the following Cauchy-Euler equation to a constant coefficient equation and hence…

Q: Solve for the 2nd order nonhomogeneous linear equation: y"+12y'+37y=10e-4t     ; y(0)=4,  y'(0)=0

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Q: Given, 1 y" +-y' + y = 0 x2 Write 2 linearly independent solutions (in the form of Bessels'…

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Q: Solve by the addition method: 4x+5y+: 12 %3D 3D 2x-y+2: = 17 %3D x+2y+2= O A. (2, –1, 9) O B. (4,…

A: Given: The system if linear equation as  4x+5y+z=122x-y+2z=17x+2y+2z=11 To find: The solution of…

Q: y" + 4y' + 3y = 12

A: here we need to find the particular solution of given differential equation. the solution is…

Q: Use Gaussian Eleminetion to solve 20+ y + 2Z =8 3y + 3Z a-4 4¢ + 24 - Z = Iv

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Q: y +y² – 1 = 0, Yı = 1

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Q: 1. y' = x3 – 2xy, when x = 1 and y = 1

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Q: y dx + (3x – xy + 2) dy = 0 -

A: As per the instruction, we will be solving only the first one. For (4),We will solve it by Exact…

Q: Solve by homogeneous equations method (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: Use the Gauss-Seidel Method to these linear equations. How many iterations will there be until two…

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Q: = -y² + 2x²y + 2x – xª, y1 = x² %3D

A: The Riccati equation is of the form

Q: Find the Solution to Homogeneous LinearEquation: (D3-3D2-3D+1)y=0

A: Given equation is D3-3D2-3D+1y=0 find the solution of the given equation.