The ODE M(z. v) dz + N(z. v) du = 0 is exact if and only if

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: If z = e'x + y In(x), find z, and z, Zx Zy II

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Q: Consider the ODE system x' = A et + 3 with A = 4 1 3 a) Use the method of diagonalization to find…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: Find the value(s) of k such that A is singular.

A: The given matrix will be singular if the determinant of it is 0

Q: Prove by mathematical induction: For Vn E Z*,7|(232 – 1)

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Q: Let x, y, z e Z Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

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Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

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Q: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

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

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Q: Determine if the ODE is a homogeneous DE. If it is, state its degree. 1. у' 2ху2 yx2 +y3 -4/(x³y3)

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Q: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

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Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

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Q: If the Wronskian W of f and g is 3e^(4t), and f(t) = e^(2t), find g(t)

A: Wronskian W of f and g is given by:

Q: For z C, show that the solutions of cosh(z) = 1 are z= i2km, for ke Z.

A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: Show that the following relationships hold. a) (1+i)™sn[ = Sn+m[ ¯ Sm| b) än+1] = 1+ an] (m) (m), c)…

A: Considering the LHS (Left hand Side) : LHS=(1+i)mSn|¯ RHS=Sn+m|¯-Sm|¯ ( Right Hand Side)…

Q: Sa 1-rh+1 Prove that E-0 ar! F,r # 1 1-r ((n + 1)a,r = 1

A: For r not equal to 1,   The above given summation is geometric progression of first term=a and…

Q: Given the bases B = {u1, u2} and B' = {u'1, u'2} for R?, where and u'1= The transition mat rix Pg-B'…

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Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p&gt;1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x&lt;0 when…

Q: © If g(x, y) = In then xgx - vgw in simplified form is [c].

A: The objective is to solve partial derivative problem and explain process.

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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

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Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: Using the technique of substitution with u = -t, the 01 / 2²1-41 des du 70 1 04/2² du ㅠ O -1 za 2²…

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Q: eb Let A E M₁ (TR) be given If AAt = On HOME JATOT prove that A = On - Does this hold if A EMn (C)?

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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: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

Q: nd C such that AC=E

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Q: Show that E(SSE) = (n - k-1), as in Theorem 7.3f, using the following approach. Show that SSE = y'y…

A: Please find the explanation below. Thank you

Q: ), P{|Zn – c| > ɛ} → 0 as n → o. Show that for any b on g, E[g(Z„)] → g(c) as n→o

A: *Answer:

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

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Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

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Q: EX: Find the Z. T. of X(X) = cas wok u(k) Soin

A: Z transform of the function

Q: Is ZXZ cyclic? [Here Z means (Z, +).]

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Q: Find the value(s) of k such that A is singular.

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Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

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Q: Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0…

A: Just multiply both sides by P from left side and set P as 2×2 matrix.

Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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Q: Find conditions on a, b, c, and d such that

A: Find conditions on a, b, c, and d such that  B=abcd commutes with both 1000 and 0001 For any matrix…

Q: асe of A is

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Q: If p(x, y, z) = x²z + ey/x, evaluate grad op at the point (1, 0, -1).

A: The function is φ(x, y, z)=x2z+ey/x

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

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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.