Find an appropriate guess for yp. You do not need to find the values of the coefficients. y" + 3y' + 2y = 5e¬* + x cos x

Q: Solve the following DE by using separation of variables or method used in solving exact DE

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Q: Solve the given diffential by variations of parameters 1. y" + y = cos x

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Q: Find a particular solution to y" + 16y = -16 sin(4t). Yp ||

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Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: You tart muesting at t=0 y co) =0

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Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

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Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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Q: Solve the given initial-value problem ) = y (y + sin x), y (0) = 1 2xy + cos x %3D 1+y? dx Upload…

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Q: y=(4x -5x +6)(e-sin 2x), then find dy at x 0.

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Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

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Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: Obtain the general solution to the equation dy dr 2+x COS x, y(0) = 2. 5.

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Q: y tan x dx + In* ydy=0

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Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: dy 29 + y tan x: dx 1 (4x + 5)? y³ cos x

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Q: 4. Find the general solution of wt Wra + sin(x +t) by using the coordinate method.

A: As mentionsed solving question 4 Given: wtt=wxx + sin (x+t)

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

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Q: Solve D.E using Exact from first order (x' +y' )dx+(2xy + cos y)dy

A: A differential equations M dx + N dy = 0 is exact if  My = Nx

Q: Find the general solution of the following equations. 4. dy - x² = x dx sin x 5. y-'dy + ye cos x dx…

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Q: . Find the qeueral solution: - 2 dy +5y = ex Cos 2x

A: Complete solution = complementary function + particular integral.

Q: Find the general solution of y" – 4y' + 5y : sin (1)

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: Given the differential equation is y"+2y'+4y=111e2tcos3t The objective is to find a particular…

Q: Use undetermined coefficients to find the particular solution to y"+ 5y' + 4y = - 500 sin(3t) Y(t) =

A: We have to find the particular solution of  y''+5y'+4y=-500sin(3t) by using the method of…

Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

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Q: Find the solution of the following Differential Equn 3) y'+2y = cos(x) 4) y' = (y-1) cot(x)

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Q: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

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Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

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Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

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Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: ution of y" + 4y = cos 2x b

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Q: The velocity of a particle moving along the x-axis is given by: v(t) = 1 cos(nt), t>0

A: Use the defination of velocity than solve the differential equation by separation of variables.

Q: Determine ?? using undetermined coefficients: 1. y'' + y' + y = 2xex

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Q: Find a particular solution to y" + 16y = 16 sin(4t). Yp

A: The given differential equation is:y''+16y=16sin4t        ...............(1)The auxiliary equation…

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: Find the general solution of the following exact differentia (e + 2ry)dx + (cos y +2a y)dy = 0.

A: As it is given the differential equation is exact si we can directly use the formula of exact…

Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: Find constants A and B such that yp(x) = A sin x + B cos x is a solution of dy/dx + y = 2 sin x.

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Q: Determine the form of a particular solution yp for y"+y cosx

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Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

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Q: Solve the given DE: dy e* – 2x cos y eу — хx2 sin y' dx ||

A: Differential equations is solved.

Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: find the general solution of dy/dx + y = 2 sin x.

A: Now comparing with Now integrating factor is,

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) : 0sxs1 :y(0) =1;h 0.5 dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

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.