5. Solve: (1 + + In x + dæ = (1 – In x) dy

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Q: K OM = (9 + x) in ; OL = (3x + 13) in %3D %3D

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Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: 1-y² L In (r* + y? +

A: Introduction: The process of determining the area of the region under the curve is known as…

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A: Following are the integrations.

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Q: 2 X- - SS. T dydx

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A: Step 3Given,2π∫14xe-x2dx

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Q: Solve the following DE using variable separable 1. dyidx = 4x + xy/y -xy

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Q: 18. y = (In 0)" > dy de = T(In 0)-1) () T(In 6)(-1) %3D

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Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

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Q: Evaluate the integrals

A: 37. ∫112142dtt+4tt38. ∫0edyy1+(ln y)2

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A: In the question it is asked to solve the equation using coefficients linear in two variables:

Q: Evaluate the following integral. 4 3е ху dz dx dy -111

A: Given: ∫-14∫13∫1ex2yzdz dx dy

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: Solve the following Exact DE using Method of Grouping. 1) (2xy + 1)dx + (x² + 4y)dy = 0

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Q: please show all steps

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Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

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Q: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

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Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: (2823 у — 3D 252*у — 6 sin 3а) dx (20x°y3 – 21a*y?) dy 4.4 - -

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Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

Q: dx 2 28 — 12х — х

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Q: The integral 2N | 6xe- dx can be done with the substitution u = and du = dx.

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Q: Solve the following integral: 1 yz²e²-y²-=*dx dy dz

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Q: The integral 4 dy dx is equal to: Select one: 12 6. None of them

A: To determine the value of the integral ∫03∫014 dy dx.

Q: dy 3 (113) _1) dri Ber roullis Solve this by using caruation. %3D

A: The equation is given by: dydx=31313-1 Assume x=1,y=3 to get: dydx=yxy13-xdydx+xy=xy14 Which is a…

Q: Solve the following intial value problem. y^(4)=-cosx+8sin2x, y'''(0)=0,y''(0)=y'(0)=1,y(0)=3

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Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

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Q: Evaluate 1- x? dx 0. by Simpson's rale with n=5

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Q: In(v¤) dædy 6. 15. Calculate ry

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Q: ne exact length of tne X = Vy (y – 3), 4sys9

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Q: 5. 4y°(x² + 4)- dy + 4xy = (x* + 4)² dx

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Q: Show that +2100 kT te kT = [0 – 0] = 0; t from 0 to o

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Q: Q/ Find an integating factor for the diff- equ. 2y dx + (3y-2x)dy20? to

A: Conversion of non exact differential equation  to Exact differential equation. Given differential…

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.