Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead of dx sinx . where Ax = 0.1, y(x = 0) = 1. And compute the relative error till the error at most 0.05.

Q: use the variation-of-parameters method to solve the given differential equation. Q. y′′+y =tanx.

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Q: determine the general solution to thegiven differential equation. Derive your trial solution…

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Q: Use integration to find the general solution to the differential equation: dx %3D y – 4

A: Given,         The differential equation is dydx=x-2y-4 .

Q: y=X+ Ci ex t %3D

A: Explanation of the answer is as follows

Q: on) solve the Differential en by using vanation of parameters - 24 (+12 yll -24¹ +y₁

A: Please see the below picture for detailed solution.

Q: By separating variables, find the general solution of the differential equation dvc = - dt RC' where…

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Q: Use the initial condition to find the particular solution of the differential equation. dy = 4xy…

A: In the given question apply the variable separable method, i.e, isolate the y terms on the left side…

Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: Obtain the general solution of the given differential equation: tanydy = sin3xdx

A: The given differential equations tan2y dy=sin3x dx⇒sec2y-1 dy=143sinx-sin3x dx    As…

Q: Solve the differential equation by variation of parameteres: y'' + y = sec(x) + tan(x)

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Q: Obtain the differential equation by eliminating a and b from the rdation y=a cos 4x +b sin 4x

A: Given equation is y=a cos4x + b sin4x find out the DE by eliminating a and b

Q: Solve the differential equation defined by x dy/dx −2y = x^6 sinx.

A: Consider the provided differential equation,

Q: Solve the differential equation by variation of parameteres:   y'' + y = sin2 (x)

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Q: Solve the differential equation below: xcosydy+sin2ydy-dx=0

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Q: Find the differential equation by eliminating the arbitrary constant  sin-1x + sin-1y = c

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Q: Solve the given differential equation by finding an appropriate integrating factor to make it exact…

A: Given equation is the linear equation  of the form  dxdy+xP(y) = Q(y)  and integrating factor is…

Q: Solve the differential equation by separating the variables.   dydx=sin(x+y)−cos(x+y)

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Q: y se, SinX+G Cnn

A: Explanation of the answer is as follows

Q: The differential equation formed by eliminating a and b from y = ae* + be* is

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Q: Determine the equation of the curve passing through the origin in the from y = f(x) which satisfies…

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Q: Q1 By eliminating the constants A and B from the equation y = Asin 2x + B cos2x, form an ordinary…

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Q: xcosydy + sin2ydy – dx = 0

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Q: Solve the differential equation using undetermined coefficients satisfying the given conditions. (a)…

A: Since you have posted multiple questions which are not interlinked so I can do first question as per…

Q: (3 şiny-5x) dx + 2x²cotydy = 0 hint: let 2 =sinu

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Q: Find the general solution of the differential equation = 6 tan(5y) using separation of variables. dx…

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Q: Solve the given differential equation by separation of variables. dy = sin(3x) dx

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Q: Find the differential equation by eliminating the arbitrary constant/s. Gedr cos x + Cge y = c1e 3x…

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Q: xcosydy + sin2ydy – dx = 0

A: First arrange it in the bernouilli equation then find its integrating factor. Then  use the formula…

Q: Find the general solution of the differential equation and check the result by differentiation.…

A: Given the differential equation:

Q: -ka dt2 Sdlve the differential equation and express the X func tion of trieonometrie func tion as

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Find the Differential equation by eliminating the arbitrary constant  Sin-1 x + sin-1 y = C

A: sin-1x+sin-1y=C

Q: Solve the 2nd order linear differential equation y" – y' = 5e* – sin2x %3D

A: The auxiallary equation for the given differential equation is given by

Q: Show that y=x and yex are lenean inde pendent Solution of the Corres pondinp hamogeneous part ot the…

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Q: Form the differential equation by eliminating the arbitrary constants y = a csc x + b cot a

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Q: У(4x + у)dx — 2(x? — у)dy %3D0

A: The differential equation Mdx+Ndy=0 is exact if ∂M∂y=∂N∂x. Compare the given equation with the…

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Solve the differential equation by variation of parameters. y" + y = sec(8) tan(0) y(8) =

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Q: Solve the differential equation by variation of parameters. y"+ y = sin(x) %3D x cos(x) y(x) =…

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Q: dy :-y = xy2 dx

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = et In(t)

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Q: Solve for first odrer differential equation    (x^2+cosy)dy+(3x^2+2xy)dx=0 where; x=0 , y=π/2

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Q: 4te dt TOT

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Q: Determine the differential equation of the family of lines passing through the origin O ædx + ydy =…

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Q: (2х — 5у + 3)dxх — (2х + 4у — 6)dy %3D 0 - -

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Q: Form the differential equation by eliminating constants a and b from y = a(b – x)(b+x) + 56.

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Q: Find the differential equation by eliminating the arbitrary constant/s. e COsX = c(1 – cos y) %3D

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Q: y'tanxsin2y = sin²x + cos²y

A: Assume t=cos2y then differentiate both side with respect to x to find dtdx .…

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given,         dydx=x5y