dy Given a DE of dr 1-z-y using simple substitution, what must be your z? z+y Answer: ||

Q: The ODE dy 4ry+5y2 can be transformed into a separable ODE in z and z by dz zy + 3z using the…

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Q: The DE : y'= e 5x-7y is seperable Select one: O True False

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Q: dy 4xy+5y? can be transformed into a seperable DE The DE: xp xy +3x2 in x and z by using the…

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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

Q: 1-y² L In (r* + y? +

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

Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: Evaluate fl. 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

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Q: dy 24. Find dr? in terms of x and y. 6-8xy 9x-5y %3D

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Q: dy Given a DE of dz 1-r-y using simple substitution, what must be your z? Ity Answer:

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Q: Find f"() if fx) = 2e* - %3D e* In 2 Ob) 20 2e* O c) 2e O d)

A: Recall:     d(eax)dx=a.eax

Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

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Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: O Find the linearization Lcx) for fex) 3x -8x+7 when a=

A: We will find the linearization L(x) for the given f(x)=3x2-8x+7 when a=-2 in the following step.

Q: i =r+ 1+1 1le n de bifureation? on?

A: This is a problem of Dynatic Model, stability Analysis.

Q: IS T Mene (R) -7 Pz(2) defined by T()= a +2bx+ (C +d )x² In lerti ble ? If so fiad its inverse thet…

A: The answer of given question is given by using some properties of inverse linear transformation.

Q: Evaluate xy ds, where C is describe by æ = 4t, y= 3t, 0 <t<1. Enter your answer as a number in…

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Q: A second solution y2 for the DE z'y" - 4ry +6y = 0, can be obtained by reduction of order with the…

A: According to quetion given Differential equation x2y"-4xy'+6y=0

Q: 5. By making a suitable substitution, find the general solution y= y(r) of the ODE dy = (y – 4r –…

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Q: Q3) Find aw dw & ar ds interms of r&s if w = x+2y +z x= y = 4r2 + In 2s & z = 4r X=- %3D

A: Given: w=x+2y+z2, x=rs, y=4r2+ln2s &amp; z=4r. To find: ∂w∂r and ∂w∂s. Solution: Partial derivative…

Q: The DE : y = e-/Y is seperable Select one: O True O False on

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Q: Expand la In 3 Inx Iny? Inz 2n 3+ 2mx+ 2lmy hz a. 2h3+ 2hx+ 2ny- 2hz In 3+ Inx+ 2hy- nz

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Q: Find the general şolution_to the following. (D* - 2D – 7D? +8D+12)y = 0

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Q: is T Mzxz Mzuz defined by T()=(* ) in vertibla? If so hind Q tb C td its inverse T-l thet is find…

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Q: One 56 Use fPicard method to approximate y when a= 2, given that y=1 when r=o and dy da

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: S(2y + 3)?/ y+ 2 dy

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Q: -3y(In x)' +3x* (In x) y' =0

A: First simplyfy the given differential equation.Then taking integral on both sides and solve it.

Q: dy 5t vi (In(t) + 1) Vi dt

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Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: Assume w = ts³, 4ts) and (x,y) = 6xy of (х.у) - 4х Find as when t = s = 1 %3D

A: Given: From the given expression it is clear that 'f' is a function of 'x' and 'y', and 'x' and 'y'…

Q: The DE : y' =e3x-7Y is seperable Select one: O True False

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Q: S- - ydx + xdy, C: y² = 3x from (3,3) to (0,0) 01 0 3 O 0 2

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Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: Q: Examine y (o.4), Using Runge - Kutta Order 4 method if X = 4n + 2

A: Given y′=4x2+2y,      y(0)=1,   h=0.1,   we have to find y(0.4).Forth order R-K…

Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: dr if r= Vs+1 dt and s=16r² – 20r 1. Find - %3D

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Q: To find ∫x3(x4−15)7dx∫x3(x4−15)7dx, you would need to use u-substitution. What u could be used to…

A: ∫x3(x4-15)7dx

Q: Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

A: These questions are related to indefinite integration, we will use use integration formulas and…

Q: Let z=xln(x2+y2-e4)-3xy, x=tes, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be4, then…

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: thereducedsystem yBY -t -t it CI

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Q: ta the téduction of order melhod, the substitution y= 5u can be used for the DE: - 3y/= 0, to obtain…

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Q: Verify by direct substitution that Un(x,y)=sinnx sinhny is a solution of Uxx+Uyy=0 for every n&gt;0.

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Q: Find KCKT) if XC2) is given by: 3. XCZ) = (Z+1)(Z-1)

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Q: Find the lenegth of the cunde 312 2 from x=o to -

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Q: - (3x + )*. Let y Then - A(Ax + +)" (8 -)", where B dy = Al 8x + xp A = B = C = D = I| || ||

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Q: 1. y(IV) – y = 0 1 y(IV).

A: The solution is given as

Q: Find the general şolution to the following (D* - 2D – 7D² +8D+12)y = 0|

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Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.