Solve the following diffential eauations a) dy + 4 y = e dy 3n2y = そ? ea3 dy C) N + 2y = そマ dn

Q: Find the Ye neral solution of the eguation. 6y"_5y_4 y =o %3D

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Q: x?y' = 4x? + 7xy + 2y² x²,

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Q: |: Use Mashematizel Induethon to solve bhe followbing; j I(2") + 2(2²) + 3(2-³)+.. .+ n(2^)…

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Q: 12. If KR= x +7, KM = 3x -5, and JL = 4x – 10, what is JR? %3D %3D

A: Given: JKLM is a parallelogram.

Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: %3D 7. If mBC = (9x – 53)' and mCD = (2r + 45)", find mBAD. E

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Q: Using modified euler's method, fihd au appn ximate Walve 84 when 4=03,given that ca dy K+y € y= 1…

A: Given that dydx=x+y and y0=1 To find: The value of y(0.3)

Q: dt (e2t + 8et + 7)ā et+4 a) 9ezt +8et+7 +C b) In(e2t + 8et + 7) + c 2 c) 5Ve2t+8e*+7 +c e4t d)…

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Q: Find the value of 20 so that Pet=11 dz (z – 20) (z – 16i) -2ni |z=11

A: Cauchy Integral formula: Let z=a be a simple pole of a given curve f(z) over a simple closed curve γ…

Q: The value of | ysin(xy)dA, where R=[1,2]×[0,1]will be.

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Q: VO sides 2. PU = 9cm and UT 6cm In the diagram below SU || QT and ST || QR. T. Q Giving reasons PS…

A: In triangle PQT SU∥QT PSSQ = PUUTPSSQ = 96PSSQ = 32....................................EQ.1

Q: Solve the dfferential equiation dy-pne™ + cosn

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Q: Use the substitutions : = ye S =X Q.3 to solve the du + y Əx PDE : %3D х, и(1, у) — сos y.

A: Using the substitutions we will solve for the PDE given as follows: ∂u∂x+y∂u∂y=x ∂u∂x+y∂u∂y=x…

Q: dy ({})y+3

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Q: Determine the solutions of the following diffe- rential eguations. X-y リー× Ae dx + e dy %3D

A: Given:- ex-y dx + ey-x dy =0 To find:- General solution of given differential equation

Q: Find U from the differential equation and initial condition. I'm know the answer but I don't know…

A: To solve below initial value problem.

Q: If æ?y + y³ = x – 1, then at (0,-1) is dz Select one: a. 0 O b.를 C.

A: Given,x2y+y3=x-1differentiating both the sides w.r.t.…

Q: csc?y dy is equal to A -у соty — coty dy B) None у сoty — coty dy D у сoty + coty dy

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Q: 8. If x = 1- 1 and y = In 1, what is in terms of 1 ? dx (B) 21 (C) -- (A) (D) 212 (E) 214

A: Given x=t2-1,  y=lntdxdt=2t,  dydt=1t Now,  dydx=dydtdxdt=1t2t=12t2

Q: Again differentiate with sespect to x we e?+ cs(xe? +e?) +C2 e? cje + C2 ze+ 2C2e? dz2 from O : cze?…

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Q: Solve the following aw dw aw. Q1) w(x,y, z) = xy²z³ + esin(x*y²z) + x² – y³ + z – 7 find ( дх ду az

A: Here x,y and z are independent variables and w is the dependent variable that depends on x,y and z

Q: Use Cramer's ru;e to fins a solution: 5x+4y=12 3x-6y=24

A: System of equations are 5x+4y=123x-6y=24

Q: C) d4 器 ★竹+ s×M 3. %3D +2x 4. If ap diffelentiat e with les Pectto Subject. 1 / 7 l

A: given,        y=x44+2x2

Q: 522 – 7z+3 dz - 12 dt 15w – 13u? + w dw f) e) d)

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Q: Given that 3xVx² + 4 dx = 5/5 – 8 what is [ 3u /u? + 4 dư?

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Q: Suppose that a?y +xz? = 3 and let u = -r³. Find the value of du when (x, y, z) = (1, –1,2). dz A) –2…

A: Given that: x2y + xz2= 3 and u=-x3 and (x,y,z)=(1,-1,2). We find du/dz ot differential with respect…

Q: Solve the following first-order linear DE's. yE) = 1 y' + (cotx)y = xcscx, %3D

A: Proceed as shown below

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

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Q: Show the following differontial quahion is hamegenous and Solve it: X*dy +C y-xy) dx

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Q: Solve the diffgerential Eauation by Separating the Vaciables ex dy 2x %3D

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Q: S T6 dar = tan-i +C 1 –1 16+z2 4 True False

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Q: V Show a c om le te solution 1/ 7 - +2

A: Given: -

Q: Find in side r=2 aren oul sde r=l+ Ges 6

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Q: 1 If Y = x? dy = ? then dz · +c O 22? O 2x 2 dy If y = 6x + 2.5x² + 7x + 2 then dr

A: 1. Given y = x2 So dydx = ddx(x2) = 2x Answer: 2x

Q: Differentiate y = (t^2+2)/(t^4-4t^2+5)

A: We have to find differentiation

Q: If A= ACH) find the A? m d2 A RT dA 2. dt

A: We have to find the characteristic equation and solve for homogeneous solution.

Q: If the substitution u= J2x+| iS used, then Só V2x+ī dx is equivalent to ?

A: Substitution will be done by the given variable

Q: 59 AM Thu Mar 4 * 69% + : 0 12. Find all solutions of the following equation on the interval [0,27).…

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Q: consider Cea) y'= */x . Classify this eg natiun wi th resput neous. For each tu erch entegory,…

A: For each category first we will check it the equation belongs to it if Yes then we will find the…

Q: In ATUV, TU II WX. Given that VT=21, VW=9, and TU=49, find WX. T W U -0 WX=

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Q: SOlve the inihal problenm. shouid be in Porm y=--. -3 dy = (38t+51) dł Y () =0 %3D

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Q: rer, Evalua den (3x1 fnd C: lve Segeant Co0) to (4,2)

A: Line Segment:    Each portion of the line segment can be labelled for length, so you can add them up…

Q: Evaluate SSS9e=+y²+=?)** dV over B where B = {(x, y, 2) : a? + y? + z? < 1}. Take = 3.

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Q: dy dr 4 - y (b) _ In(교2 + y? + 1) dr dy (a)

A: Evaluation of the double integral

Q: 8l Aply ithe / Jesidues de eualuate Calular Cosnede It 20 (oS0+ a?

A: To evaluate I=∫02πcosnθdθ1+2acosθ+a2 using calculus of residues.  Let us consider  z=eiθ Then, on…

Q: d. ý <(1+s)y, ,h=o•2 yCi) = e

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Q: II filled in formula answer = 2TTrh+2TTI V = Bh %3D 14 %3D ni2.E to auib61 6 iw lesmuso 1o 1o sbom =…

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Q: Solve all other parts of each AJMP, Round off your answers to the nearest whole number. 12. ZP =…

A: I have appended the formula used in the solution part

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

A: Ring Theory.