express z1z2 and z1/z2 in the form a+ib. Q. z1 =− 1+3i, z2 =2−i.

Q: Solve the general solution of the given DE: dyldx = (2y/x) + (3x/2y).* %3D

A: Suppose any linear differential equation can be written in the form of  dydx=fyx then it is a…

Q: Find all integral solutions of the linear Diophantine equations 6x + 11y = 41

A: We recall a standard theorem about Linear Diophantine Equation and then use that theorem to solve…

Q: (b) For what value of u have the following homogenous equations non trivial solutions? . (1 – µ)X1 +…

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Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: If the auxiliary roots of a certain HLDE with constant coefficients are 2, -3, and -3, then the…

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Q: 2. Find the general & particular solution of the DE, 4- 16 + 16y = 0 with the given that y(0) = 2…

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Q: Find the value(s) of z which satisfies the equation |z| 2 + 1 + 6i = 6z

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Q: Let P(z) = z100 + 8z10 – 3z³ + z² + z + 1. Find the number of roots of P(z) (solutions of the…

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Q: Find a general solution. u"+21u 0 u(t) = ]

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Q: Which of the following Diophantine equations cannot be solved? (a) 12x +4y = 40 (b) 65x + 15y 35 (c)…

A: To determine the Diophantine equation ax+by=c has a solution, identify the values of the constants…

Q: Find the general solution to the given Euler x?y" – 3xy' + 9y = 0

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Q: A) Find the values of x and y that satisfy the equation: In(3 + j4) +7+1²2= j(x − y) + (4x + j2)…

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Q: Show that r =1+i, x2 = 1- i is a solution of (3+ i)x1 + (1+ i)x2 = 4 + 4i

A: The solution is given as

Q: Consider the DE: x' -[2, x, with solutions x = and x2 = 12 a) Verify that x, and x, are solutions to…

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Q: 1. Get the following equations in "y =" form: 4y + 7 = 3x and 4х + Зу %3D 9 Format Font | Size •BI 口…

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Q: Given z = 3– 4i and w = -1- 2i, compute the following and express your final answers in the fe-n a +…

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Q: Let w e H and suppose that (1+ i)w(1+ 2j) = 1+ k. nd w (your answer should be in the form a + bi +…

A: Given function is, 1+iω1+2j=1+k

Q: Which of the following is a proper substitution to solve the following Bernoulli's equation? zy'-…

A: To find the proper substitution to solve the following Bernoulli's equation:xy'-7exy3=11y

Q: SOLVE THE FIRST ORDER DE. (x² – 3bxy + 2b²y²)(xdx + ydy) = xdy – ydx

A: Given differential equation is (x2-3bxy+2b2y2)(xdx+ydy)=xdy-ydx

Q: Suppose that f(t) = e (1−2i)t is a complex solution for an unknown second-order linear equation…

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Q: 1 1 dr = In a. find the exact value of a. %3D V16+9x? 19+4x*

A: Here we will solve for 'a' step by step answer given below,

Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

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Q: The solve of the equation: In(z+ j)= ja / 6 Is 1 + j 2 2 ||

A: Given:           So,               ln(z+j)=π6j⇒z+j=eπ6j⇒z+j=cosπ6+j sinπ6⇒z+j=32+12j⇒z=32-12j So, it…

Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

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Q: x²y" – 5xy'+9y = 2x

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Q: Use the substitution x = et, to solve the following Cauchy-Euler equation: x²y// – 4xy/ + 4y = x³ In…

A: We will find out the required solution for given Cauchy Euler differential equation.

Q: Find the solution of the Euler-Cauchy equation x²y" + 0.6xy' + 16.04y = 0.

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Q: x²y" + 2xy + (x² − 1)y=0.

A: Given eq. is x2y''+2xy'+x2-1y=0             1

Q: Reduce the following equation to a canonical form and hence solve it: 3u +10u xy +3u vy = 0 xXx ху…

A: See the solution in the given fig.

Q: Find the general solution of u(x, y) for : Uxy = x A uxx + u = 0 A xuxy + 2uy 1

A: Consider the given differential equation. xuxy+2uy=1                  ……(a)

Q: 1. a) Find , if y= (x² – 11)“ dx b) Express (8/30) (2Z60) in the form a+ bi c) Solve (2+3) +3/- x+iy…

A: The detailed solution is as follows below:

Q: If A = x° yz? î – 3x² z³ j + yz? k , then a² A at the point (1,0, 1) will be дхду 3 î -3) -3 î

A: The vector A is A=x3yz2i-3x2z3j+yz2k find ∂A∂y=x3z2i+z2k ∂2A∂x∂y=3x2z3i the point 1,0,1…

Q: Q1/ Consider the following equation Uxx +Ury - 2u vy +1=0 1) Determine the type of the equation. 2)…

A: Given PDE is uxx+uxy-2uyy+1=0 comparing with Auxx+Buxy+Cuyy+f=0 We have   So…

Q: Verify that z 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2+ 41 also a solution?

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Q: g. y= 2x 1 h. y =x i. y = x - 3 j. 2. y = --x+ 5

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Q: 4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' -…

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

Q: Find the general solution of the following ODOS: (а) x2y"-Зху'+4у3D0, х>0.

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Q: Let d = gcd(a, b). If (xo, Yo) is a solution of the linear Diophantince equation ax + by = c, which…

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Q: Calculate 1₁ ₁² ² a feas = e¯² ds for the piece of the cylinder x² + y² = 16 for 0 ≤ z ≤ 7.

A: we have to find the ∬Se-zdS for the piece of the cylinder x2+y2=16 for 0≤z≤7

Q: What values of α and A make y=Acos(αt) a solution to y′′+6y=0 such that y′(1)=2?

A: The solution of differential equation y’’+6y=0 is

Q: Find the solution of the Euler-Cauchy equation x?y" + 0.6xy' + 16.04y = 0.

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Q: 1) Rewrite c(r) = 2+5z+2 I-3 in the form y= q(x) + He where r has degree less than b.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: x + 3y + z = 1 2x + 5y – z = 1 x+ 2y + 3z = 5

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Q: Solve the following equation uxx + Uyy = 3x - 5y with the conditions for the square plate u(0,y)=0…

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Q: 4. Determine the unknowns using [X] = [A]¯*[B] and [A] by the adjoint method. %3D 10x + 2y – z = 27…

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Q: 18. Determine the roots of the auxiliary equation of y" + 3y" – 4y' – 12y = 0 (а) —3, —2,2 (b) -3,…

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Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

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Q: Which is the solution to the equation 7n 37 2sin22x + 3sin2x + 1 = 0, x = 6

A: 2sin22x+3sin2x+1=0 Put x=7π6 in the given equation, we get…

Q: Find the solution of the given syst- x+3y +3z=2 x+4y +3z=3 x+3y +4z =1

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Q: Find дхду of z %3 In (x? - у) -2х дхду (x²–y)² 2ху дхду (x² –y)² 2х дхду (x²–y)² O. 1 %3D дхду…

A: Givenz=ln(x2-y)To find∂2z∂x∂y