Given the differential equation (ye-* - sin x) dx – (e ¬*+ 2y) dy =0, what is the value of f'(y)? (A y2 (B - 2y 2y -y2

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 the differential equation using undetermined coefficients method y''+4y=2x sin(x)

A: Given that y''+4y=sin2x Let y=emx Now  m2+4=0m=±2i Therefore the general solution,…

Q: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

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

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Q: Find the differential equation whose solution is given by y = C,et*cos3x + C,e*sin3x

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Q: Xoly-y dx-Jx.ye dxz0

A: Given:            xdy−ydx−x2+y2dx=0

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 using variation of parameters, what is a possible value for u' for the differential equation y' +…

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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: What is the solution to the differential equation 2 = 2xy satisfying the boundry condition y = e…

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Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: dy sin(x - y), use the substitutions To be able to solve the differential equation dx

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Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

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Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: What is the standard form of this linear differential equation in one variable. Y + 1)dx + (4x – y)…

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Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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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: y' cosx f. -=cos y

A: The given differential equation is,y'cos2x=cosy

Q: Find the differential equation by eliminating the arbitrary constant/s. y = = Aex cos x + Bex sin.x…

A: We differentiate the number times as the number of arbitrary constants present in the equation and…

Q: What is the general solution to the differential equation (2xy – tan(y))dx + (x² – xsec?y)dy = 0? |

A: First we have to show that the differential equation is exact. Then we find the general solution of…

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

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Q: What is the linear differential equation of dy/dx+2xy+xy^4=0 using dv/dx?

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Q: xcosydy + sin2ydy – dx = 0

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Q: What is the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0?

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Q: dy -2 sin x where y (5 = JT dx

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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: The Bernoulli's form of the differential equation xdy - [y + xy³ (1 + ln x)]dx = 0 is

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Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

Q: xcosydy + sin2ydy – dx = 0

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

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

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Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

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Q: Use separation of variables to find the general solution of the differential equation. y- dx 4…

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Q: what is the particular solution to the differential equation dy/dx=3sin(x)(2-y)with the initial…

A: You need to apply variable separable metod to solve the given differential equation.

Q: What is the particular solution to the differential equation [x+(1+x)y] = 12 with y = 0 and =0 when…

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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: The Integrating Factor of the differential equation dy dr y = 14x? is x-14 25 e5z

A: The given differential equation is,  dydx-5xy=14x2To find its integrating factor.

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

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Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

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

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Q: 9. The differential equation (3y cosx+4xe" + 2x'e' dx + 3(sin x +1)dy=0 is exact because aN

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Q: particular solution to the differential equation \frac{dy}{dx}=(x−3)y with the initial condition…

A: Given differential equation  dydx=(x-3)y also y(0)=2.

Q: What is the General and Particular solution of the Differential Equation 2x(y+1)dx-ydy=0? Where x=0…

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Q: By using variation of parameters, what is a possible value for u, for the differential equation y' +…

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Q: For the differential equation y' = 2y - x, draw line segments representing the slope field at the…

A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

Q: xydx + 2(x2 +2y)dy=D0; when x= 0, y= 1

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Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

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Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx