Integrating Factor by Inspection a.) y(x²−y² + 1)dx− x(x²−y²−1)dy= 0 b.) y²(xdx + ydy) + (x² + y²)(ydx−xdy) = 0

Q: Using integration by parts to solve f S and letting u =-, x2, then v = f(x) is %3D

A: Integration by parts is used to integrate an expression that is a product of 2 functions. The…

Q: 30x 2. (a) Use a suitable substitution to find | dx. V1– 2x (b) Use Integration by parts to show…

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Q: 1) f(x) = *+x*, r<1 x'+1 x21 df = ?, x1 dx a) f'(x) = %3! b) f'(1) = dx I = ?

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Q: 2 y

A: According our guidelines i solve only first question.For second solution please resubmit again…

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

Q: Using S- dx x√√x-1 Rationalizing Sfy)dy, find ffy)dy Substitution

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Q: B. Integrate the following using the basic rules of integration and substitution. 1. fx² + 5x3 –x-3…

A: Given problem:-

Q: (2xy +x? +x*) dx – (1+x?) dy = 0. |

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Q: 9] Expression for R(x) in f(D)y = R(x) which is solvable by the method of %3D undetermined…

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Q: y® cos(3y) dy

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Q: xsin x -dx, a > 0. x +a 15. Evaluate by method of residues |

A: Residue theorem

Q: Using integration by substitution in ſ x³(x6 – 2)³dx, what is du? A. xdx В. бх5dx С. (х6 — 2)dx D.…

A: ∫x5(x6-2)dxPut x6-2=udifferentiate…

Q: Finding a General Solution Using Separation of Variables. dy/dx= (x-1)/y3

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Q: D. Fina the total differential of the function xye¬(x²+y*),

A: Given: f(x,y)=xye-x2+y2

Q: Using Integration Techniques solve for the implicit solution. (xycos(x) + 1)dx + (xsin(x) + cos(x)…

A: Given differential equation is, xycos(x)+1dx+xsin(x)+cos(x)+y4dy=0Here…

Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

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Q: B. Integrate the following using the basic rules of integration and substitution. 1. fx2 +5x-x-3 dx…

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Q: 3. dy - 2** + e 2x cos (x) + Cos(x) y Fuctor8 Integrating

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Q: 6tan¬1 dw w

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Q: Test for exactness (2ysinxcosx - y + 2y?ey )dx = (x - sin?x - 4xye*y )dy %3D solve exact de,…

A: First we have to check exactness then we solve the differential equation.

Q: 6. f In² x dx

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Q: 2x2-6x+8 3-x-V 1-x² The value of the integral dx is

A: We have to calculate the given integral

Q: dx x+x4/3

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Q: 2 Integrating factors found by inspection.: fr-y+1tr-af²-y²-1ky =0

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Q: tergal / 1 dx using the residue theorem. (x2 + 1)3

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Q: dx Half-angle Substitution cos x +sin x-1

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Q: dx secx + 1 Transforming - -z² A 1+z² B z²+z 1-z² 1+z² Ⓒ 1- D √ -dz -dz -dz - 2z² 1+z² -dz using…

A: Here, the given integral is: I=∫dxsec…

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

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Q: Integrating Factor by Inspection: 5. (xy-2y²)dx - (x²-3xy)dy = 0

A: (xy-2y2)dx-(x2-3xy) dy=0x(y dx-x dy)-2y2 dx +3xy dy=0dividing by xy2;(ydx-x dy)y2-2x dx +3y…

Q: Using integration by parts, | - | x sin(x²) dx x* cos(x²) dx = k – Then k is?

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Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: Show complete solution for verification: ydx + (x + x3y2)dy = 0

A: The equation given to us is ydx+(x+x3y2)dy=0             (1)

Q: Question: * Using integration by parts, integrate S In 5x dx A. xln 5x – x+ c с. 5xInx - х+ с в. х?…

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Q: Test for exactness (2ysinxcosx - y + 2y?e*y )dx = (x - sin?x - 4xyey")dy %3D solve exact de,…

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Q: 5.Integrating factor by Formula 2 (2y? + 5xy – 2y + 4) dx + x (2x + 2y – 1) dy = 0

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Q: 16) Approximate ,xer'dx Using Gauss-Legendre 3 points formula G3(f)

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Q: Integrating Factor by Inspection: 7. xdx + ydd = (x² + y²)dx

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Q: ution of yl = x+xy2 W

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Q: dx (4x²-9)3/2 17.f

A: The given integral is I=∫14x2-932dx

Q: Using Rationalizing Substitution S- O In(y) + C O Arctan(y) + C O2Arctan(y) + C O2ln(y) + C dx…

A: ∫dxxx-1Substitute y=x-1→dydx=12x-1→dx=2x-1dy=2∫1y2+1dy

Q: x3 dx Using integration by parts to solve J- V4-x2 and letting -÷x², then v = f(x) is U = - %3D

A: We use integration by parts

Q: dw 3. (w² +4)Z

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Q: Using Gaussian integration, (a) 2 ¹₁ f(2x + 3) dx (c) 3 ¹₁ f(3x + 2) dx the integral ff(x) dx is…

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Q: Integrating Factor by Formula b) y²cos xdx + (4 + 5ysinx)dy = 0

A: Given: y2cosxdx+4+5ysinxdy=0 An equation of the form Mx,ydx+Nx,ydy=0 is said to be exact if…

Q: dy

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Q: 14. Use integration by parts to find S x cos x dx . You MUST show the four substitution parts (u. v.…

A: Integration by parts ∫u dv=uv-∫vdu

Q: FINO THE PARTICUCAR SOUTUON OF THE DIFFERE NTIAL EQUATION -スx =e + hx t子x-9 dx² -2x dy e AT X=0,9=0…

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Q: II. Test for exactness. If it exact, solve. 1. (x- 2y)dx – (2x + 5y)dy = 0 2. (4x³y-18x² + y)dx+ (x*…

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Q: TOPIC:EXACTD.E., LINEARD.E., INTEGRATINGFACTORS FOUND BY INSPECTION 2.Obtain the particular solution…

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