(-2e* sin(y) – 4y)dx + (-4x – 2e* cos(y))dy=0 Use the exact differential method to find a function F(x, y) whose level curves are solutions to the given differential equation. F(x, y) =

Q: dy - sin x - y tan x = 3 e dx solution of differential equation is %3D

A: Introduction :

Q: Find a differential equation of order one whace solution ū given by * Sin + In x +C %3D y= Find a…

A: The differential equation of order n for any function f(x) is fn(x).

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

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

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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: Is (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Exact differential equation- A differential equation of the type Mdx+Ndy=0 is said to be exact if,…

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: dg dx =g (4-8)4=x* 2.

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Q: (3x* – 1)y=x- Zx° †X 2. Find the differential equation of all straight lines at 2- unit distance…

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Q: dy -=x' +y+xy Solve the differential equation dx condition (0) =-1 and 0sxs2 with step length 0.4 by…

A: Given differential equation is, dydx=x2+y+xy With the initial conditions, y0=-1 and 0≤x≤2 We can…

Q: The solution for the differential equation (D2 + X²)y = 0 with boundary conditions y(0) = 0, y(3) =…

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

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Q: The solution of the differential equation using variable separable +8 sec y = 0 is da dy O siny = 8x…

A: Divide by secy and multiply by dx the get the variable separate

Q: 1. Find the general solution of the linear differential equation using undetermined coefficients,…

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Q: Consider the equation (y² + xy)dx + (5y² – xy + y° sin y) dy = 0 • Show that the original DE is not…

A: NOTE: Refresh your page if you can't see any equations. . compare this equation with  so here we…

Q: 9. Solve the differential equation (2 sin?y + 4x² sin y)dx + (3x sin y cos y + 2x³ cos y) dy = 0…

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Q: (-2e" sin(y) – 4y)dx + (-4x – 2e* cos(3))dy =0 Use the exact differential method to find a function…

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Q: ind the general solution of the (3x - y -1) dx - (x - y + 3) dy = 0 differential equation.

A: Given: The differential equation is 3x-y-1dx-x-y+3dy=0                       ⋯1 To find the general…

Q: A first order Bernoum's differential equation is in the form 2. The Bernoulli's form of the…

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Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: 1) (-2xy j dx + (Siny-x²)dy -X²³ 2) dy + 3xy dx = x edx g) (3x - 2y + 2) dx + (3Y-Zx-2) dyz 4) (y +…

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

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Q: Consider the equation (y² + xy³) dx + (5y² – xy + y³ sin y) dy = 0 • Show that the original DE is…

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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: Use separation of

A: Given,                     7dydθ=eysin2θysecθ.

Q: Using the substitutions 2- sin y and dz- cos y dy, the differential equation (3sin y - 5x)dx +2x cot…

A: The solution is given as

Q: 3. (х - у)ӑх + (х — у+2)dy %3D0 (Homogenous) 4. 2(2ху + 4y — 3)dx + (х + 2)?dy 3 0 (Non-exact)

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the general solution of separable differential equation when x=1 and y =1               dy/dx =…

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Q: Find the particular solution of the differential solution dy/dx=x^2(y+2) given that the point (0,5)…

A: Given,  The differential equation  dydx=x2y+2   Point 0, 5 lies on the graph of the solution  We…

Q: dy --y= 2sin 3x dx first-order linear differential equation y(0) = y, find the solution that meets…

A: Consider the provided first order linear differential equation, dydx-y=2sin3x It is in the form…

Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION ху 1. (x + Vy2 + 1 ) dx - [ y + ] dy = 0 /y² + 1

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Q: Find a linear homogeneous differential equation with constant coefficients so that the general…

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Q: (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Given differential equation is  1+exydx+exy1-xydy=0 Which is in the form of Mdx+Ndy=0. where…

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: dy/dx+(sinx/cosx)y=2cos^2sinx-1/cosx of first order linear differential equation y(pi/4) = 3√2 find…

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Q: 7. Consider the differential equation y(1-ysin(x))dx + (2x+3ycos(x))dy = 0. a) Find an appropriate…

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Q: 1. (х — у)dx + хdy %3D 0

A: 1) Given:            x-ydx+xdy=0           xdy=y-xdx           dydx=y-xx  set y=rx…

Q: Particular Integral for the differential equation (D² + 25)y =(cos5x) is given by a. -xsin5x 5 b.…

A: Option; b is correct.  Given differential equation ; (D2  + 25 )y  = cos5x Let D = m; Auxiliary…

Q: Find the value of n that makes the differential equation xn (3x+4y)dx +(2xn+1 +2y)dy = 0 exact.…

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Q: Find the particular solution to the differential equation. 2y2 dx = 3x2 dy when x = 2, y = -1 %3D

A: We first separate the variables2y2dx=3x2dy2dxx2=3dyy2then integrate both…

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

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Q: Verify that the indicated function y = y(x) is an explicit solution of the given first-order…

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Q: 1 Solve for the differential of y when y=sinx, x=÷, and dx=-

A: Solution. A is true.

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: 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: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

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

A: Given that:  4dydθ = ey sin2θy sec(θ) So, by using variable separable, we getyey dy = 14. sin2θ…