If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove that x,y,z are in A.P.

Q: find An eignuector of the matix 12 17 2 VZ V3 19 2 J3 -VIT -2 Ji

A:

Q: 2. Solve the following Cauchy problem: Uu = Uzz -0 0, u(x,0) = x – a², u(x,0) = 4x, -00 <x < 0. %3D

A:

Q: Under what conditions on A and B does the B.V.P x'y" - 3xy' +3y = cos x, solution, no solution ,…

A: Given equation is, x2y''-3xy'+3y=cosx Take the homogeneous term, x2y''-3xy'+3y=0 Take y=xn,…

Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

A:

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: Find all angles between 0 and 2n satisfying the condition V2 COS T = Separate your answers with…

A:

Q: nts A and B have symmetry with respect to the ) (9, 2) (х, у) %3D -) (0, 8) (x, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

A:

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

A:

Q: 1. E is a triangle with vertices (1,0,0), (0, 3,0) and (0, 0, 2), with 8(x, y, z)=xz+1.

A: Note: As per our guidelines we are supposed to answer only one question and the rest can be…

Q: 16. Use Theorem 12 to show that 2n r=0

A:

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

A:

Q: 2.2 Find upper bound of 2+4 (z - 3i)3 +1 where C is the circle |2 – 3i| = 4.

A:

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

A:

Q: Use Fermat's Theorem in your proof that Vn E Z>², 2 is irrational. I

A:

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

A:

Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: b) By using De Moivre theorem, calculate in the form of a + bi: 4. i) (VZ – iv2)* | ii) (1– i)6

A: Given (2-i2)4 &amp;   (1-i)6

Q: The standard form of 3dy-xydx = 3y3e4x/3  by Bernoulli's equation is:

A:

Q: 1. how that { cos(Inx), sin(Inx)} is a fundamental solutions set for x²y" + xy' + y = 0 on the…

A:

Q: In A XYZ, ZZ is a right angle and mZX = 53°. Which statement is true O cos 53* YZ %3D XY XZ O tan…

A: From the given figure representative diagram is shown below:   With respect to ∠53°.…

Q: State where in the ty-plane the hypotheses of the Existence and Uniqueness Theorem are satisfied for…

A:

Q: Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and…

A:

Q: 18, where 1, 2, 5. Consider the solutions are there uation 2i Eg + Tg + Tar uovenba (a) if z1, r2,…

A:

Q: 2.2 Find upper bound of 2+4 (z – 3i)³ + 1 where C is the circle |z – 3i| = 4.

A:

Q: Hence, using chain rules find y' i. y = sin(2x² + tan(6x² – x)),hint: u = 2x² + tan(6x² – x) ii.y =…

A:

Q: Find the residues of each of the fellowing functièns at its. poles. e •f(z)- 22+3 4. ans : ri=7/4 ?…

A:

Q: (b) Show that U (x, y) = eu cos v, V(x, y) = eusin v are conjugate harmonic of each other if f = u +…

A: It is given that,  f = u+iv  is analytic. We have to show that,  U(x, y) = eu cos v  and  V(x, y) =…

Q: Prove that z'e'-z = 1 has exactly two roots inside the circle |z] = 1.

A:

Q: 5. Determine if u and v are orthogonal u = (cos, sin 0,-1); v = (sin 0.- cos 0,0)

A:

Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

A:

Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: Let r(t) (sin(4t), cos(41), sin(4f) cos(81)). Find the point where r(t) intersects the xy-plane on…

A:

Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

A:

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

A:

Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

A:

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

A:

Q: 2 de Evaluate the intergal using the residue theorem. 12 + 6 sin 0

A:

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y"…

A:

Q: a. Let z1 = 2 – 3i, z2 = 3 + 4i and z3 = 1– V3i. Find z1z2 + z3 then sketch it on Argand diagram.

A: Simplify Z1Z2 + Z3 in simplest form and convert it into polar co-ordinates.

Q: Prove that: Z,Z2 =r,r2[cos(0, + 02) + i sin(0, + 02)] 1.

A: NOTE- As we are allowed to answer one question in one session so, i have answered first one for you.…

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A: