z = – 3i is a solution of z² + 3i = 0 z³ + 3 = 0 z² +9 = 0 z² – 9 i = 0

Q: Q1: Use Gaussian Elimination solve the following equations: 3x1 – 0.1x2 – 0.2x3 = 7.85 0.1x1 + 7x2 –…

A: The given system of equations         3x1-0.1x2-0.2x3=7.85         0.1x2+7x2-0.3x3=-19.3…

Q: IV. Solve for x using the fact that if a" = a", then v = w. (Show solution) 6) 5x-1 = 0.042x %3D 7)…

A: Use the fact, "If av=aw, then v=w" to solve the following equations for x.

Q: Which is NOT a solution of V2- i ? C. -0.4717 + 1.2196i D. -0.8204 – 1.0183i A. 2.2094 0.3442i B.…

A: To find the nth root of a complex number we have to use de'Moivre's formula :…

Q: 2. Find the general solution of y' = x² – 2xy a. y==(x² – 1) + Cor* b. y = x² – 1) + Ce* c. y =;(x²…

A:

Q: 2. Find the general solution of Ei-0 (2)*y(n-1) = 0. %3D

A:

Q: w + x + y + z= 6 x + 3y + z = -14 w + 2x -3z = 12 2w + 3x + 6y + z = 1

A:

Q: Solve for x, y, and z by any numerical methods that is applicable. Use x = 2, y=6, and z=5…

A:

Q: 5: The real values of x and y for which the equation is (x + iy) (2 – 3i) = 4 + i is satisfied, are

A: Introduction :

Q: Find c such that the equations below have no solutions. x + 2y = 1 cx + 10y = 4 Then c =

A:

Q: 5x 7y %3D a. 5x + 7y = O Infinitely many solutions O No Solution O Unique solution - 5 7x b. 3y 19x…

A:

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: IV. Solve for x using the fact that if a" = a", then v = w. (Show solution) 1) 0.10-* = 102x+1 2) 2…

A:

Q: z= - 3i is a solution of z2 +9 = 0 z2 -9 i = 0 %3D z' +3 = 0 z2 +3i = 0

A:

Q: Find the general solution of x'1 = x2 - x1 + t, x'2 = x2.

A: The given differential equation are - x'1 = x2 - x1 + t   and   x'2 = x2 We can re-write the…

Q: a) Give a particular solution for y" – 2y' + y = 3e*. b) Give a particular solution for y" – 2y' + y…

A:

Q: (c) (i) Solve the linear equation: 2(3 – x) = 3(x + 5) (ii) Expand (x + 4)(x – 5) and use this…

A: (a + b) × ( c + d ) = ac + ad + bc + bd

Q: z=- 3i is a solution of z² – 9 i = 0 z3 + 3 = 0 z2 +9 = 0 z2 + 3i = 0

A: Given: z = -3i   To find: The given z is solution of which polynomial from the given polynomials.

Q: nen z=x+iy Q2. Solve the following equations: 1- z* +4 = 0 2- z- (1+i)8 = 0 %3D 3- zz - 2iz = 17 -…

A:

Q: (b) Use Gaussian elimination to find the values of x, y and z: x+2y+3z=10 -x+y+z=0 y=z=1

A:

Q: 30. Discuss the behavior of the solution of x" – x + 3x² = 0, x(0) = 0, x'(0) = 1. %3D %3D

A:

Q: 10 -1 27 -3 -6 x2 -61.5 1 1 5 x3 -21.5 2.

A: Given :   Matrix equations is given.

Q: Q1 : Find the solution of x, y, z by using Gramer's Rule. 3x + 2y – z = 1 x - y + 5z = -2 2x + y = 3…

A:

Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

A:

Q: 23. Find the general solution of x (x 2)y" – (x? – 2)y' + 2(* - 1)y = 3x²(x 2)°e*, %3D

A:

Q: Find the General Solution of (D² + 5DD' + 6D²)Z = 10 cos(x – y)

A: Given partial differential equation is D2+5DD'+6D'2Z=10cosx−y. We have to find the general solution…

Q: 6 csc 0 - -2sin 0-√2sin Øcsc 0 + csc 5x 7 7 Sx 7x A) B) 14 4 x 5x D) No solution. O KIM

A:

Q: 2.N.CN.7 Which of the following equations does not have any real solutions? * x² – 4x + 2 = 0 x2 -…

A: We use root formula for quadratic equation

Q: Use the method of undetermined coefficients to find a particular solution to the given higher-order…

A:

Q: All solutions of the equation z* – 16 = 0 are - z = 2i, z =-2i Ob. z = 2, z = -2 z = 1, z=-1, z=-i,…

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: 2.0 Solve for x , y, z, and w by Gauss Elimination Method Method Given : 6х-2y + 2z +4w 16

A: The solution is given as

Q: - 1 3 x': 5 - 3 *** 1 1 - 2t 5 The particular solution is x, (t) = and x2(t) = .

A:

Q: Yk+1 – kyr = A(-1)*(k – 1)!. The solution to this latter equation is (k-1 Yk = (k – 1)! A(-1)*(i –…

A: To find solution of these type of equation we have to apply recurrence relation.yk+1-kyk…

Q: z= - 3i is a solution of z2 +3i = 0 z2 - 9 i = 0 z2 +9 = 0 z3 +3 =0

A: Third option is correct

Q: 5. Find the general solution of yy' + y² = x a.y = x -+Ce-2* b.y² = x ++ Co-* c.y² = x -+ Ce-2r…

A:

Q: Solve z? – 2z+4 = 0. Let u and v be the solutions of z? – 2z +4 = 0, then: A. u = -1 – iv3 and v =…

A:

Q: 1 2 -2 1 A = [4 8 -8 4: Describe all solutions of Aa = 0. Express your answer as a linear…

A: Given: A=12-2148-84 To Describe: Describe all solutions of Ax→=0→.Express your answer as a linear…

Q: 9 -4 2 x' = X = 14 -9 The particular solution is x, (t) = and x2(t) = -

A:

Q: 2x^2+4=2(3-x^2y)y' A. Prove or disprove if the given DE is exact. B. If it is an exact DE, find its…

A: The equation  M(x, y)y' + N(x, y) = 0, or in the equivalent alternate notation M(x, y)dy + N(x, y)dx…

Q: 5. Given the General Solution the DE, Identify the roots * y = C1e¬2x + C2cos2x + C3sin2x O A) m1=…

A: Here, the solution to the DE is: y=C1e-2x+C2cos 2x+C3sin 2x...(1)

Q: z=-3i is a solution of z2+9=0 z' +3 = 0 z² + 3i = 0 z² - 9 i = 0

A: Let z is a complex number. We can represent as z =a+ ib. Where  i=-1

Q: a) Give a particular solution for y" – 2y' + y = 3e*. b) Give a particular solution for y" – 2y' + y…

A:

Q: 2y" — 12" + 4у' + 72у %3D 0

A: Given ode is homogenous. We will find root of this ode then we write solution.

Q: 9. Find the general solution of (2ху - у? +у) ӕ+ (3x? — 4ху + 3х) фу - 0 А. хtу?(х - у + 1) 3D с В.…

A:

Q: Q5. Solve the Euler-Cauchy equation xy" – 5xy + 9y 0 A. В. Solve the Legendre's equation (1-x²)y" –…

A: Given,  (A) Euler-Cauchy equation            x2y''- 5xy'+ 9y = 0. (B)  The Legendre's equation…

Q: 3i is a solution of z2 - (1+ i) + (2 + 2i ) = - i %3D

A: False

Q: ii. Find all solution of z+2z +1+i =0 .2

A:

Q: 1 (i) Given that 2 Sx x 4 = show that 5x + 2y = -3. (ii) Solve the simultaneous equations 2x x 4" =…

A: Properties of surds and indices ax x ay=ax+y a0=1 If ax=ay  then x=y (ab)c=ab x c

Q: 2у" + 3у' + у%3D 3sin x + xe

A: