Be. La ecuación diferencial (4x²y² + 6x y)dx + (5x³y + 8x²)dy = 0 tiene un factor integrante de la forma: µ(x,y) = xPyª. Calcular p yq y obtener la solución general. %3D

Q: Find and at the given point without eliminating the parameter. x = Vi, y = 21 + 309; † = 1. dy

A:

Q: Given a = 8t – 22 and y = 64 sin t %3D %3D - dy dx d'y %3D da?

A: Let x = 8t - 22 and y = 64sin(t) Differentiate x with respect to t dxdt=ddt(8t-22)=ddt8t-ddt22dxdt=8…

Q: FIND THE GIVEN DIFFERENTI Homogeneous Eguation ( 3x + 4y) dx - dy -0

A:

Q: I=Jx Incx) dx, where b is a constant with %3D bフ)

A: Intregation of product of two variables is given below

Q: Differentiate y = Arccot (4x x) 6 VX (A y' 1+ 16 x3 6 VX 1 + 4 x (B y' 3 6 VX y' = 1 + 4 x3 6 VX D…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Jy csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соѓу+ coty dy D) None E у…

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Q: Find the cifferential dy of the given funddtion. (Use "cx" for dx.) y- dy

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

A:

Q: Given x 13t - 12 and y = 169 sin t %3D %3D dy %3D dx dy dæ?

A: Given that       x = 13t - 12   and   y = 169 sin t Here we have to calculate     dy/dx         and…

Q: c) x+2y) dA, where D is bounded by the parabolas y=2x2 and y =1+x?.

A: C) The area D bounded by the parabolas y=2x2 & y=1+x2 is as shown below. The red graph is of…

Q: Transform the equation (a'y – 3y) y' + æy variable separable form o into a %3D | f (x) dx + g (y) dy…

A: We know,  A variable separable differential equation is the method to solve differential equation in…

Q: If z= t(x,y), where X = rCOse and y= rsine, %3D Show that 12 dz 12 dz dz dr dz del + dx

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Q: Given z = 11sint + 18 and y= 11 cost + 45 (*) da %3D dt (i) (**) dy (0) dz %3D

A: Given that, x and y are parametric functions

Q: Given z = 15 In(t) and y = 225 t then find %3D dy dx d'y dr2

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Q: 4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y >…

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Q: .. Evaluate (x+y) dx+xy dy where C is the parabola y = x², x : 0 → 2.

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: x+ y dydx = Inß ху %3D Find B.

A: The objective is to find the value of beta.

Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: state the arder, degree, and linearity of the filowing differe ntial squtions ) ax* 9 + asx) : 3x-4…

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Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

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Q: Transform the equation (2?y – 3y) y' + æy³ = 0 into a variable separable form - f (x) dx + g (y) dy…

A: The solution is given as

Q: Find the conditions such that the equation M (x, y) dx + N (x,y) dy = 0 mogeneous and exact.

A:

Q: Solve for if y- Ina 2- y?. da MCQ3.pdf dy 2y +1 dx dy 2y +1 dx dy dæ -(2y+1)x 1 dy (2y+ 1)a TERIRS…

A:

Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

Q: Transform the equation 2 (y + 1) dr – ydy = 0 into the form of variable separable. O 2zdz y (y+1) dy…

A:

Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: h) $ dz =. 1) where C is a positive contour outside of a point z=i= (0,

A:

Q: Detrminc Partiular solurion y?dx + (x*+ 3×y+4y?) ay:0jx=2,y=1

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Q: By algebraic substitution, the integral dx dx is converted to: 4+Vx dy y+4 2 dy y+4 ydy y+4 2ydy y+4

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Q: Given the DE. 3dy + ydx = (1-2x)y4, Rewrite the DE into Linear Form at v O dx-v = 2x+1 dx-v=2x-1…

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Q: Find the extremum of f(x,y) = 5x²y² +4y² + 6x². %3D Answer:

A: The given function is f(x,y)=5x2y2+4y2+6x2 .......................... (1)

Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Use the equation e = 2xyz+1 to find %3D az/əx and əz/ay.

A: We have to find

Q: Let z = exsec y Find d²z dxdy and d²z dydx

A: .

Q: Find y' and y". y = Vx In y' y" %3D II

A: we have ,  y=xlnx y'=?y''=?

Q: х2, у3D 12 — х, х 3D 0, around line y — -2

A: the function given to us is y = x2 and the line about which it revolves is y = -2 we have to use the…

Q: Use Green's Theorem to evaluate |. (y? – 6y) dx + (y³ + 10y²) dy where C is shown below.

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Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

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Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.