Solve the difference equation Ywa + 2y, = 0 (k > 0) given that y, = 1 and y, = ,2.

Q: The solution of the 2" order IVP y" - y = 0, y(0) = 0 and y' (0) = 1 is

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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: Solve using implicit differentation.    x ey = 3x-3y

A: Given;   x ey = 3x-3y

Q: Solve x?y" – 2ry' + 2y = x³ In x by first finding the complementary solution and then using the…

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Q: y" – 2y + y = 1+x?

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy + y?

A: Idea: after separating x,dx and y, dy terms together. we take integration on both sides . after…

Q: (² + 1)³yy'(t) = 1(y² + 4)

A: Given:- (t2 +1)3y y'(t) =t(y2 +4)  To find:- General solution of given differential equation

Q: Obtain the general solution y

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Q: y" - 6y' + qy 2,

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Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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

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

Q: Find the solution by using Solution of 2nd order D-Es 2 X ý XỨ ty - xy + y = Lnx -

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Q: D. y" + y’ - 3y = 4sin 2x

A: This question is related to differential equations, We will solve it using given information.

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: find general solution. dr/dt= -2tr,         r(0)=ro

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Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method *

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Q: – kz = 0, -z= 0, solution then

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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: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

Q: Solve the following equations  by the method of undeterminedcoefficients. y" + y = e2x

A: The given equation is y" + y = e2x Substitution of y=ex into the differential equation yields the…

Q: solve for y in terms of t or x, as appropriate.

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Q: How do I integrate the following equation? U(z)=2.8*exp(-z/6300)

A: Consider the given equation as Uz=2.8*e-z6300

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method

A: We have the following equation in two variables : y2 + y = x + ln(x) + ey - x2   As there are two…

Q: [Q4] Applying the method of variation of parameters, solve x'y" - 2xy'+2 y = x' sin x

A: The solution is given as

Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

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Q: Find the general solution using the method of variation of parameters (1) y" + 9y = 12 sec 3x

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Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: (b) Solve y" + e*yf + (1 + x²)y = 0, %3D x = 0, if y(0) = 1; y'(0) = 0. %3D

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Q: Find the general solution using the method of undetermined coefficients. dx +7x=8e° dt -41

A: Answer

Q: Q.4 Use the method of separation of variables to solve : xyu̟ +2u, =0, U(x,0) = 3x* . %3D

A: Standard partial differential is given as: p∂u∂x+q∂u∂y=r Lagrange method for finding solution for…

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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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: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: Obtain the general solution valid near the origin: 2y'+9ху'-36у 30

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Q: find the solution  x2y"+xy'+x2y=0, Assuming y(x)= sum n=0 to inf. anxn Solve correct answer do…

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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: y" + 2y" + y" = x + eX %3D

A: Given the differential equation y'''' + 2y''' + y'' = x + ex We find the particular solution form…

Q: 2. (6x + y²)dx + y(2x – 3y)dy = 0

A: In this question, we need to check whether the given equation is exact or not and then find the…

Q: 4. Solve for x. MZWYX = 56x +1 M2WLX = 58x - 1 4. Solve for x Y

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

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

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Q: Solve for general solution using the variation of parameter method x²y" – 2xy' + 2y = xFe* find the…

A: Given DE is x2y''-2xy'+2y=x5ex. Use the variation of parameters method to solve the DE.

Q: ty" – (t+ 1)y' + y = t?

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Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: Obtain the general solution valid near the origin: 8x?y" +10xy' -(1+x)y=0

A: Power series solution of the differential equation

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y (0) = 0.4, y' (0) = –0.4, y" (0) = -0.4

A: The Symbolic form of the equation is D3+D2-2Dy  =4e-2xcos x Auxiliary  equation is D3+D2-2D=0…

Q: Apply Variation of Parameters to find the general solution. e* у"- 2у'+ у 3 1+x?

A: Given y''-2y'+y=ex1+x2

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.