Which of the following is a fundamental set of solutions of y" + 6y' + 5y-0? a) O {e', e} b) {e,3e} c) none of these d) O {et,e } e){e,-v2e-}

Q: 2) [10] Justify the steps of the following theorems, first directly and then indirectly. Include…

A: We have the following rules in logic theory. a) A conjunction m∧n can be decomposed to m as well as…

Q: 70) ydx +zzdy

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Q: -64m12+ 24m10 1) 4m

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Q: 6) If the roots of an ODE are rl =1, r2 = 1, r3 = -1, what should be the solution of it? a) Cex +…

A: The general solution of an ODE having repeated roots is given below. Let the roots be a and a.  In…

Q: True or false? Justify. a) x2y5 = (xy)10 b) 5u2 + 5u3 = 10u5 c) (3r)29s2 = 81r2s2 d) 3…

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Q: ii. Consider the matrix B Find the characteristic polynomial of B and substitute in B like you did…

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Q: 50) If f(x) = r° cos(x³), then f() (0) is d) 5! а) 0 b) 1 с) 3! e) f(5) (0) does not exist. 51) If…

A: f(x)=x3cos(x3)f(x)=x3∑n=0∞(-1)n(x3)2n(2n)! f(x)=x31-x62! +x123!+...f(x)=x3-x92!…

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A: Part 2: Explanation:Step 1: Identify the contour C:The contour C is defined as the set of complex…

Q: -3 • Determinant of N = 1 -2. 1. -5 7 3. 5 4. -7 2.

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

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A: As there are three variables we have to find the differentiation of z with respect to X thus we…

Q: dy the differential equation is called the Riccatti equation. = p(x)y² +q(x)y +r(x) dx a) Let y1 be…

A: Consider the given differential equation, (a) Since y1 is the solution of Riccatti equation, Let,…

Q: -2=sec 0 %3D A) 5n 7n 5n B) 3 3 6 6 2n 4n C) 3 3 2n 7n D) 3 6 4) -1+5csc 0 = 1 + 3csc 0 TC A) (0} B)…

A: to solve trigonometric equations.

Q: Solve the Euler Cauchy Equation a) 3x²y" + 11xy - 3y = 0 1

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Q: Os) Solve fer the real mumbers x and y 2 25 (2+i)2 (2-i)2

A: We have x2-y2+i2-y2-x2-i2=225i-12y2-y We now simplify this equation.…

Q: 2. K42

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

Q: 0) (1 b) |0 0 0 ) 5 1 1 5. Solve; a) 6 - 1 2 1 0 0 0 4 55

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Q: 76 39) 461 5x 41) 5x 43) (a2). 20² 45) 2k. (3*°)' 47) (4x³)'x"

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Q: -) V = [V₁, V², V3, ₁] = is и 21 21 30 Io 11 02 O u= [ ] linear combination of V or sto 9

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Q: a) AUB=An B 1 1 1

A: Since you have posted a multiple question according to guildlines I will solve first(a)   question…

Q: The solution of the differential equation (x + 1)+o + 1) = 0 is A y=2+x B. y= C. y = x(x- 1) D. y =…

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Q: What is the general solution for a (x³ – 1)10 dæ? 1 (a – 1)" +C O 10(23 – 1)° + C o 1 (2³ – 1)" +C…

A: using method of substitution

Q: 1(42). M = "+ x/F + 78 +1=24 S

A: According to answering guidlines we are doing first question if one or more question given

Q: Al6)- (;) ) A (;) - (:) |zuso -gsino) f) A(3); (xsine +yuno

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Q: iv. Make a conjecture about matrices and their characteristic polynomials based on the computations…

A: Let us consider a 2×2 matrix A defined by A=ab0d                      (i) The characteristic…

Q: S 22² +2+1 dz, where с Z² +4 b) Compute i) ( = {Z : 121=1} ii) C = {z: 17-i |=2} 17 (iii) C = {z :…

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Q: 12) If a, b and c are the roots of x' – 2 x² + 3 x – 4 = 0, find the numerical value of a’ + b' +…

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Q: b) Compute S i) C = √z: 121=4} 22²+2+1 dz, where iv) c=fz: 121=4} 22+4 ii) C = {z: 17-61-2} \ii) C=…

A: Step 1: Use Cauchy's integral formulaintegral cf f(z)/z-z0 dz = 2.pi.i.f(z0) here f(z) = given…

Q: 2 x + 4 y + z = 3 3 x + 5 y+2z = 2 3x+ y+ = 1 thesolutionis :

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Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Prove that dz 7-9 (2-2)"dz =0 b,ony integer # -I 2. And Evaluate WHER E Ĉ is the are of the cycloid…

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