The equation y" + y' – 2y = sin x is called a differential equation because it involves an unknown function y and its derivatives y' and y". Find constants A and B such that the function y = A sin x + B cos x satisfies this equation.

Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION 3. (x + 3)cos ydx - [siny In(5x + 15) - y] dy = 0

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Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: Find the general solution of the first-order linear differential equation for x > 0. (Use C for any…

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Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

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Q: y = C, cos 3x - C sin(-3x)

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Q: dy sin x 3) dx y=2cos sin x- 1 of first order linear differential equation COSx COsx y(7/4) = 3/2…

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. y¹= x(2e + c) 2. y = Ae³x…

A: 1. y-1=x2ex+c Note:     Multiple questions are given, we are answer with only one question. If you…

Q: Determine the particular solution of y' sin(2y) – cosx = 0,x ==when y = 0 %3D %3D Identify the…

A: Here the given differential equation is in variable separable form. So here we can use variable…

Q: Form the differential equation by eliminating the constant 'a' from r=2a (sin 0- cos 0)

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Q: Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is…

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Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x=(0, π). is:

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Q: The general solution of the differential equation is given. Use a graphing utility to graph the…

A: The general solution of the second-order differential equation, from the characteristic equation,…

Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied 1 sin 2 1…

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Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: f(x)=∫f'(x) dxf(x)=∫(16x3-6x)dxf(x)=16x44-6x22+C              (∫xndx=xn+1n+1)f(x)=4x4-3x2+C where…

Q: sin x sin y y' cos x cos y

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Q: [cos y + 1]dy + [tanx (siny + y)]dx = [sin y cos x + y cos x]°dx gettyimages When:x = 0;y=

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Q: the given differential equation has a particularsolution yp of the form given. Determine the…

A: Given: y'' + y = 2 cos x + sin x, yp= Ax cos x + Bx sin x To Determine: the coefficients in yp and…

Q: Determine the general solution and the particular curve that goes through point (0,0) of the e* cos…

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Q: A solution for the differential equation is y = eux A1 sin (vx) + A2 cos (vx), where m and n are…

A: We will find out the required values.

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

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Q: y = C, x? sin 4x + C2x² Cos 4x

A: The equation is y = C1x2sin4x+C2x2cos4x

Q: y' + (2 tan x)y = - cos'x

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Q: verify that the given equation is a solution of the differential equation.(elimination of Arbitrary…

A: The solution is given as  y=-cos(x) ln(sec(x)+tan(x))                   (1) Differentiate equation…

Q: Find the solution to the differential equation that satisfies the given condition. I am having…

A: Given differential equation can be written as Integrating both sides , we get

Q: The general solution of the differential equation by direct method: dy sec2 x dx 1+ 2 tanx y =…

A: According to the given information, it is required to find the general solution of the given…

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

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Q: Find constants A and B so that y = A cos(x) + B sin(x) satisfies the differential equation y" + y' –…

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Q: Consider a first order differential equation. y(-x sinx + 2 cosx ) dx + x( 2 cosx)dy = 0 a) Find the…

A: Given , Differential equation is  y-xsinx+2cosxdx+x2cosxdy=0 Now ,we write the given equation of the…

Q: Find y2 for differential equation if yI is given: ху" — 20у'%3D 0 Y1 = 15x13 -

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Q: verify that the indicated function is an explicit solution of the given differential equation…

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Q: dy cos(x). + y sin(x) = sin²(x) cos(x) y³ dx

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Q: Solve the first order linear differential equation. dy - (cotx)y = sin³ | dr

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Q: (x4cos y) dy + (x + 3x3sin y) dx = 0. Show that this differential equation is not exact. Find the…

A: given  (x + 3x3sin y) dx+(x4cos y) dy= 0 to show differential equation is not exact solution general…

Q: Y = CI cos 3x + C2 sin 3X

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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: Show that the differential equation (- y² – y sin r + x²)dx + ( cos x – 2xy – 2021y²) dy = 0, | is…

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Q: (メyーx+24 -2) dx- (x+ 4x) 0

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Q: Find the differential equation whose solution is                    y = A cos 8x + B sin 8x

A: We have to find the differential equation whose solution is  y = A cos 8x + B sin 8x  Here ,  2…

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

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Q: Determine whether the given differential equations are homogenous or not homogenous. If the equation…

A: A first order differential equation is homogenous if it can be writen in theform dydx=Fyx

Q: he of the curves corresponding to different values of C in the general solution of the differential…

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Q: Determine the form of a particular solution for each differential equation 1. y" - 2y + y = 10e -2x…

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Q: What is the general solution with steps of the differential equation y’=sin(3x)y+y+sin(3x)+1

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Q: obtain the linear differential equation with the real, constant coefficients that is satisfied by…

A: Solution.

Q: 2x sin2(y) dx − (x2 + 12) cos(y) dy = 0 is given by  ln(x2 + 12) + csc(y) = C.   What is the…

A: bring every x terms one side and y terms another side.

Q: )(I + cos x) y Sin?x + Sin? x cos x -y sinx

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Q: 2 sin x Show that y is the solution of the differential equation xy'+y=2 cos x.

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