The DE yy" + ay +2xy=0s O None of these. ODE. inear of order 3 O oDt of order 3. inear and homogeneous. O oDe of order 2. Inear but non homogeneous O 0DE of order 3 non-inear.

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: One of the following ODE is a linear DE of second order O x³y"-3y'=e*+xy O None of these O…

A: We are given some ODE and out of which we have to identify which ODE is linear DE of second order.…

Q: Given IVP y'=t-t²y, y(0) = 1, 0≤t≤ 1.8, N=3. The value of y(0.6) using Runge-Kutta of order four is…

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Q: If the seeedof an dbjectis given by ve) what is its eoríthen x al a to dime + = 2 it the object was…

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Q: Which of the following is homogenous of smallest degree? (A x+y B) In x - In y x4+y4 x-y D Vx-y

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Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: _4. Arg (zz) = 0, whenever :+0. _5. Arg(=)= arctan 2| for x +0, wherex= Re(z) and y = Im (z). 6. Arg…

A: This is a problem of complex analysis.

Q: Q1) prove the following below i). Corr(X , Y ) ∈ [−, 1, 1] ii) E(X|Y) = E(X) or E(Y|X) = E(Y) ⇒…

A: We need to use the concepts of Variance, Covariance and Expectations to solve given question.

Q: Which of the following is homogenous of smallest degree? x-y (A x-y В Inx - In y Vx+y x4+y4 D X

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Q: Find y(0), y(1), y(e), y', y", and a formula for y(") where n is a natural number. Use DNE, Does Not…

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Q: -tan(z) %3D z*+cos(z) dx Select one: O a. None 5sin(z) Ob. ²+coz² (z) Oc. O d. 0

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Q: 4946が-8+Sy = o R = x?,2メ-1 %3D 21) メダー-SXy+$y= 2 LAX

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Q: 2. Which of the following is correctly matched? O z'y" - e"y" + sin r(y') = 0: linear, third order O…

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Q: O Verify that you (-00, os). Cos (zt) is a salution to y"- Sy= -9cos(2€) on

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Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

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Q: The oDE dy -(x +り +5} SeP arable The is

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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 yy" +4y +2xy=0 is O None of these. ODE of order 2, linear but non-homogeneous. O ODE of order…

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Q: Q2) Discus the existence and uniqueness of the following IVPS: y = x + ys y = x tan (i) (ii) y(1) =…

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Q: The following statements are all false. For each statement give all reasons why the statement is…

A: The differential equation can be linear if and only if the dependent variable and it's derivatives…

Q: e sin(y), I: ,III: y = 7" cos(y+5), IV: jý = e' b) Which of the following ODES is not separable but…

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Q: 1 2 Let the adjoint of A = be Adj(A) t Then, what is 3 1 che sum of x and y? 22 - O A) 0 O B) -1 O )…

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Q: Which of the following PDEs cannot be solved exactly by using the separation of variables u(x, y) =…

A: Differentiate the equation ux,y=X(x)Y(y) partiall with respect to x, y to obtain the expressions of…

Q: Find the right match for the following ODES in the dropdown menu y = y" sin(x) + e* + 2 Choose... 令…

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Q: -Skatch the reglén of Etyndtion , reversed the order of itegral and evaluade dx dy 7 | +

A: We have to sketch and after changing the order of integration evaluate it.

Q: The DE yy"+4y +2xy D0s O None of these. O ODE, linear of order 3. O ODE of order 3, linear and…

A: Given- Consider the differential equation y2y'''+4y'+2xy=0. To Find- The order of the above…

Q: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

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Q: Derermine the soluhi on to the followingsystem Thy 'X +3y +23=5 Thg: 2X-y- 43=4 5メ+y-63=13 %3D %3D

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Q: Consider the 2nd order ODE: d y + ну %3D 0, хE (0, L] х€ [0, L] dx2 where, M, is a constant. The…

A: Idea: consider the three cases for values of u. then solve the differential equation.

Q: Determine whether the following DE is Ordinary or Partial DE. 1.) y''-(y')3+y= sin A 2.)…

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Q: One of the following ODE is a linear DE of fourth order Oxy-3y'=e*+xy² O None of these O xy"-3y'+y…

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Q: The DE (y")3+ y= 0 is %3D O ODE, non-linear of order 2. O ODE, linear but non-homogeneous. O ODE…

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Q: 13. What is f2sinx cos x dx? 2cos.x A. +C In 2 C. 2cos.x B. +C In 2 D. 14. Which of the following…

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Q: | dr = 1 in the following sense: for any ɛ > 0, there exists Ro > 0 so that for any R> Ro, •R 금 de 1…

A: Solution: We have to prove that the integral,                                      ∫1∞1x2dx=1. We…

Q: dy The ODE dx 4.ry+5y2 xy +3x2 can be transformed into a separable ODE in z and z by %3D using the…

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Q: 10 Given: OA 1 OB 1 Prove: 1 = Z3 A D. 1818

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Q: A closed Lo t it he f hale n tervad as not Horneamorphic an open intrval open

A: 9) To prove that  every closed interval is not homeomorphic to either an open interval or half open.

Q: e) Eirnd the intigal to 大アーム 2-4 a) Use thesubstidien u= ☆

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Q: 7 - Which of the following is an exact ODE? 063 a) O 3y dx – 3x dy = 0 b) O (x + y) dx - dy = 0 %3D…

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Q: ,32 Let C: z-il=3 and I = -dz. Then %3D z2 1=0 None of these O I= 4nti O I= 6ni O I= 8ni

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Q: əz az +Y ay ax then x- If Z = tan-1(2) O 1 O 2

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Q: Find y for the following ey ex-e %3D Select one: 1+y O y= x +y O y = ex-y exy xexy+eY Oy= -yew xexy…

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Q: The DE (v'")³ + y= 0 is O None of these. O ODE, non-linear of order 3. O ODE linear and homogeneous.…

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Q: 1. (xy + x)dx = (x²y² + x² + y² + 1)dy ,2

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Q: VneN 1+E, i i! = (n+ 1)! Vne N24 n!> 2" Let x€ R,-1. Prove that Vn eN (1+x)" > 1+ nx

A: 1. The statement, P(n) : 1+∑i=1ni·i! = (n+1)!  We have to show the statement, P(n) is true for n ∈N…

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Q: 1.) Find the First denivative sof y= Arcos(x) 42) Find the Finst denivatveOf wt nt bri7 (8 リ=(メ)Inメ…

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Q: Sketeh and evaluate the reverse in begral 9/x Jy de

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Q: 2)If X is exponentiol with porameter A ond Y is expom with parame ter B, ond X &Y are inde pent,find…

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