Obtain a numerical solution of the differentia I dy equation: - +2y=1 using the Runge Kutta method in the range x 0(0.2)1.0, giver the initial conditions that x=0 when y 1

Q: find the seril solution of the equation y``+  4xy = 0  at the neighborhood of the  point  x0 = 0

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Q: Find a formula for the curve y = f (2) given that its slope at the point (x, y) is y² (2+ sin x) and…

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Q: dy dx =x√√√y; y(2) = 4

A: Variable Separable Differential Equations The differential equations which are expressed in terms of…

Q: Express (x + 4/x)dy/dx - y = 1 in the form y = f(x) where the curves passes through the origin.…

A: Given differential equation : x+4xdydx - y = 1                    ...........( 1 ) Multiplying both…

Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: 3 5) ax tây là 3y = 12 x+³y=9

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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: In how many ways can four distinct numbers be chosen from the set {1,2,...,14} so that no pair among…

A: solution:- Probability when all four chosen numbers are not consecutive = 1 − Probability when all…

Q: Use variation of parameters to find a particular solution of y" - y =

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Q: ng the method of undetermined coefficients, find the particular solution y, for the NHLDE Y'"-…

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Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: 12. y = 3t 1+t³ X= 3t² 1+t³

A: We can find y' using chain rule as below.

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: What is the function of the graph? Select the correct answer. Oy-x? - 82? + 5x Oy-6x-8x3 + 5x y-x° -…

A: Facts : 1. Complex roots always occur in conjugate pair. 2. If the polynomial has degree 'n' : A. n…

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: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

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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: Consider the IVP: y= 3z – 4y-2, y(2) = 3. A) Use Euler's method to obtain an approximation of y(2.4)…

A: The given differential is y'=3x-4y-2  , y2=3 we know the Eular method is yn+1=yn+hfxn,yn

Q: plot solution curves for each of the initial conditions on one set of axes. Experiment with the…

A: Given that, x'=-tx;x0=-3,-2,-1,0,1,2,3

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

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Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

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: 1 Given: y = 4x4 Find: y' 4x4

A: Derivative

Q: Find y as a function of tif y(3) = 8, y'(3) — 9. Y - 49y"+126y + 85y = 0,

A: Find  as a function of  if  ,  .

Q: Solve the equation with Lagrange to find general and particular solution y = (2 + y')x + y'2

A: Given: Equation y=2+y'x+y'2 To find: General and particular solution using Lagrange's method