Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(‡)=C − x y O arctan (=) = C - x² - y² O 2arctan(;)=C− − y O 2arctan ²) = C - x² - y² Y

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Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: Verify the exactness of the given function (1+ex/y)dx+ex/y(1-x/y)dy=0 and then write the complete…

A: Solution: The objective is to find the general solution of the given differential equation

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A: The given differential equation is d2ydx2-2dydx-3y=cosx. We have to find the solution of the given…

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A: Given integral, ∫02∫012y2+x2+3dydx The objective is to evaluate the integral.

Q: (D² +1)y = sec x. %3D

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Q: Find the solution to the Bernoulli equation: dy/dx + 2y/x = -x²y³

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A: D2+2D+5y = sinhxcan be written as:

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Q: Solve y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0 using the substitution Z = 2 x y

A: Given that y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0  Therefore, we have  y (1 + 2 x y) dx + x (1 – 2 x…

Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

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A: Expand the left hand side expression and isolate the variables x and y.…

Q: (c) Find the value of √a²-x² Sa giving your answer in terms of a. 1+ 2(x + y) x² + y² dx dy,

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Q: Solve (3x²y³+4xy)dx+(3x³y²+2x²)dy=0

A: Let us considre the differential equation Mdx+Ndy=0 The equation is exact ∂M∂y=∂N∂x The solution of…

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Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

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Q: 2 (х + у)dx dy 1. 3.

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Q: Q9// find the general solution (sec°x + (cotx)y)dx + (Insinx)dy = 0

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Q: Q2) Solve (y+ysin x) dx - (cosx- 2xy +) dy = 0

A: Given differential equation is  y2+ysinxdx+-cosx+2xy-1y2+1dy=0 Comparing it with Mdx+Ndy=0, we get,…

Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

A: Solution :

Q: 2. Solve the DE: (2x + dx + 2y ) dy = 0 1+ x?y? 1+ x?y?

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Q: Find dydx for…

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Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

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A: We have to draw