Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

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Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

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Q: The special integrating factor of y'dx+(3xy + y² -1dy = 0 is: a. e3y b. Зу С. У d. y-3

A: Solution

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A: Consider the given integral is, ∫2ydx+3xdy The above equation is of the form M=2y and N=3x. Then, by…

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A: The solution of the problem is given in the next steps.

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A: Given: xyy2+1dx+x2y2-2dy=0, y1=1 ⇒xy3dx+xydx+x2y2dy-2dy=0 ⇒xy2ydx+xdy+xydx-2dy=0 ⇒xy2 dxy+xydx-2dy=0

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A: Image is attached with detailed solution.

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A: we have to find the region of integration

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Q: xy dx+ (xsg'4y)dy=o suiteble integrating factor and then, exact dfferential equchoms end generel…

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Q: dz = arctan ду G) dz Find: dx 2x 2y dx x²+y² x²+y² dx dz y %3D = dx x²+y² dx x²+y²

A: given,        z=tan-1xy

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Q: differentiatin, detamina dy of ; dx y= [at) (Xts) (a-z) (x-+)

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: factor

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A: find the integrating factor (xy2-y)dx + (x2y-3x)dy = 0

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A: Given differential equation lnxdxdy=2xy3

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A: Draw the given equation of the curve x2+y2=64 and the given points. The given curve is between…

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Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

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Q: Find the integrating factor of y(2x - y + 1)dx + x(3x – 4y + 3)dy = 0 Oy? 2x О ху Oy

A: See the details solution in below

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A: Given,

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Q: Find the integrating factor that makes the equation xy^3+(x^2y^2+1)dy/dx=0 exact.

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Q: Hw #4 ( 2 xy +y -tany) dx+(x²-x tany tSeiy )dy =o ??

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Use the method discussed under "Integrating Factor found by Inspection". y(x³ – y)dx – x(x³ + y)dy =…

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Q: ii- (x* + y) dx - ry dy = 0, y(2) = 1 (using Integrating Factors)

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Q: Find the integrating factor. a. (xy + y2)dx + (x + 2y- 1)dy = 0

A: We have to solve the problem

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A: To solve the given line integral.