(-2e" sin(y) – 4y)dx + (-4x – 2e* cos(3))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) =

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

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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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A: Given: Differential equation: y" + y = cscx, 0 < x < pi One solution of differential equation…

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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,…

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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

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Q: Find the particular solution to the differential equation: dy dx 3x2 cos? y. Solution passes through…

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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: c) Find a homogeneous differential equation whose general solution is given by y = c,x-1 cos 3lnx +…

A: Let's find.

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

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A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

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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

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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…

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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: (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: 1. (х — у)dx + хdy %3D 0

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

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Q: Consider the nonhomogeneous second order differential equation a°y" – xy' + y = nT +0, x > 1.

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A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

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

A: The given differential equation is: -2ex sin y-4ydx+-4x-2ex cos y dy=0

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

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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.

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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…

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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…

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