F(x, y) = (xy² – x5)i + (x²y + y®)j f(x, y) = + C

Q: f(x,y) = e (3x² + 3y2)

A:

Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: Transform ϕ (xmyn) ydx + ψ(xmyn) xdy = 0 to the type variables separable by the substitution z =…

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Q: 1+vx [8] Find y" of y =

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Q: Solve For the orthogonal trajectories (a+x) y² = x² (3a-x)

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Q: 2 (d) T (x) = Væ + 9Væ7

A: T(x)=x+9x73-2x25Formulaamn=amn1at=a-tddxx=n xn-1

Q: Solve: (xy – 1) dx + (x² - xy) dy = 0 %D |

A:

Q: Determine C when x=y=0 (xy + x)dæ = (x²y + æ² + y³ + 1)dy

A: Given that xy+xdx=x2y2+y2+x2+1dySolution…

Q: If f(x,y)=x²y³+x4y, find f XX 2y³ + 12x²y 2xy³+4x³y □ 6x²y 6xy² + 4x ³

A: Topic = Derivative

Q: Examine the function f(x, y) =-3x-4y+15x - 16y + 6 for relative extrema.

A: Here we have to find relative maximum.  The solution is in both 1st and second steps.

Q: Find the maximum value of the function f(x, y) = xye-(²x+3) in the first quadrant.

A:

Q: Eliminate the constant: 3x 3x y=c₁e³x. + + c₂2 ve ³x схе 3 Oy" + 6y' +9y=0 Oy"-6y'+9y=0 Oy"-4y+3y=0…

A: It is given that,y=c1e3x+c2xe3xwe need to eliminate the constants c1 and c2

Q: The temperature is T(x, y) = (x-1)² + y² degrees at any point (x, y) on a triangular metal plate…

A:

Q: Transform ϕ (xmyn) ydx + ψ (xmyn) xdy = 0 to the type variables separable by the substitution z =…

A: Given differential equation is 2+4x2+yydx+x3ydy=0......1. Compare equation 1 with Mdx+Ndy=0, we get…

Q: What is the domain of h(x, y) = Vx - y?

A: Given: hx,y=x-y we know that for domain of square root function inside of root not has to be greater…

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: (X²y² + 1)dx +2x²dy =0 use the substitute xy=u

A:

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

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Q: Find R of the function Y = f(x) = vx %3D

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Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

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Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: dy 3(x+y+1)2-(x +y- 1)² dx

A: Given :

Q: The productivity of a manufacturing company is given approximately by the function f(x,y) = 20x y0.5…

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Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

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Q: S sec? (3 – 2t)dt

A:

Q: Consider the initial value problem: y-y+8, 0sts 1, y(0)-1 The approximation of y(1) by using…

A: