2) Determine k such that kx² – 4x+= : 0 has real and different solutions.

Q: Prove that there are no integer solutions (x, y, z, w) to the equation x³ +y³ 3z²+9w² +3. =

A: The given equation is x3+y3=3z2+9w2+3. We have to prove that there is no integer solution to the…

Q: b) Consider the second-order DE. y+25y = 0 rE(-00,00) Show the zero's of the solutions separate each…

A: Given differential equation is, y''+25y=0 We know that the solution to a homogenous differential…

Q: If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.

A: To compute y'

Q: -X - 2xe 73Xs =l =10. %3D Jordan elimination

A: Topic :- Matrix

Q: Let (c1, c2) be a solution of the 2 × 2 system a11x1 + a12x2 = 0 a21x1 + a22x2 = 0 Show that for any…

A:

Q: Axk + 2xk + k +1 = xk+1 + xk + k +1 = 0. cion to the last equation is %3D

A: Given, let the function f be equal to△yk2; therefore, equation (6.52) becomes…

Q: Prove that there exists at least one solution to the equation 4x+ 3x +1 = 4x2.

A:

Q: Find all solutions of x2 - x + 2 = 0 over Z3[i].

A: Given: Z3i=a+bi|a,b∈Z3       =0, 1, 2, i, 1+i, 2+i, 2i, 1+2i, 2+2i We have to find all solutions for…

Q: Solve this problem About Faktorial with the full step, thank u Prove that :…

A: Note: There seems to be a typo in the question k!(k−2)!(k−1)!(k−3)! and the actual question should…

Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

Q: Suppose z 2- 3i and w = - 5i. Find: W-Z ?

A:

Q: Q 4. (a). Show that fog = 4x² – 1, if ƒ(x) = 4x – 5 and g(x) = x² +1.

A: a. Given: The functions fx=4x-5 and gx=x2+1, To find: f∘g=4x2-1, Formula used: (f∘g)(x)=f(gx).

Q: If x, y belongs to Z prove that the equation x^2+4x-8y=11 has no solution

A: The given equation is, -----(1)

Q: Show that x = e4t is a solution to x"" – 12x" + 48x' – 64x = 0. Show that x = et is not a solution…

A:

Q: Prove that the equation 3x² – 3x + 2 = 0 has a solution on interval [0; 1].

A:

Q: Find the 4 - x' -x²(4 – x²) = 2 i5 (4 - x*) + C 3 x²(4 – x²) 5 3 15

A: Please see the solutions below.

Q: 9. Find the general solutions of X' = AX with A =

A:

Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

A:

Q: Verify that yp = x2 + 3x is a particular solutions of y" − 6y′ + 5y = 5x2 + 3x − 16

A: To verify yp=x2+3x is particular solution of  y''-6y'+5y=5x2+3x-16       (1)

Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: 3. Verify that 3e-2x +4e* is a solution of y"- 3y' + 2y = 0.

A: We have to verify that 3e-2x+4ex is a solution of y'''-3y'+2y=0

Q: prove using the IVT. 2x + 3x = 4x has a solution.

A:

Q: Show if z = 2 + 4i satisfies z? – 4z + 20 = 0

A: To show that a value or number satisfies an equation, we substitute the value in the equation and…

Q: Prove that if b+ 6 < 0, then x + bx + 5= 0 has at least one real solution.

A:

Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

A:

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

A:

Q: 2. Solve using Gauss-Jordan Elimination and check using Cramer's Rule. X1 + 5x2 – x3 = 7 4x1 + 3x2 +…

A:

Q: 3. Verify that 3e 2x + 4e* is a solution of the y"-3y'+2y=0.

A: We have to verify if the given is a solution to given differential equation or not.

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

A:

Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

A:

Q: y3-3ax2+x3=0,then

A: Given:  y^3 - 3ax^2 + x^3 = 0

Q: 2. Σ--1)k , k%3D k+1

A: The given sequence is ∑k=0∞-1kkk+1

Q: Find the positive integers m such that t2x"+tx'+(t2-m²)x = 0 has a nontrivial solution such that x…

A:

Q: 25. If ā = -j and b = 2x +5y, express and y in terms of ā and b.

A:

Q: 1. Find the first-order derives: III. y = (2x* – 5)(3x5 + 12) IV. V4x? + 7+ 5-x° + 15x – 30 5x+ 4x3

A:

Q: Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)?

A:

Q: Suppose that X is a (A = e-100, p = 3e-100)-BCP. %3D What is P(X(1)X (2)X(3) = 4)?

A: Correct answer is 4.

Q: (2) Determine k such kx² – 4x +- = 0 that has real and different solutions.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)m3 3Inx: = 2Iny Then is

A: This is very complicated &amp; lengthy problem.So I can do it in Advanced Mathematics.

Q: Prove that there is a solution of the equation 2° + x² + 4 = 0, x in R.

A:

Q: (2) Determinek such kx - 4x+- =0 that has real and different solutions.

A:

Q: Find the number of integer solutions of X +x, +x, = 10 subject to the conditions given. a. 저20,%…

A: Integer solution

Q: Prove that the equation Z = 1 has no ++ solutions in positive integers x » Y, Z.

A: Assume some value and substitute it many times taking different domains like integers, whole numbers…

Q: 3- Prove that y=x is a solution of (x³ + 2x?)y"+ 2xy'- 2y = 0 and hence find the general

A:

Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: = 3e2x and y,, = x² + 3x are respectively solutions of у" - бу' + 5у -9е2х y" – 6y' + 5y = 5x² + 3x…

A: General solution y(g)= y(h)+y(p)

Q: Solve the equation forX, given that

A: To show that the given matrix B commutes with the other two matrices, B=abcd commutes with 1000  and…

Q: 2. Solve using Gauss-Jordan Elimination and check using Cramer's Rule. X1 + 5x2 – x3 = 7 4x1 + 3x2 +…

A: 2. Solve using Gauss-Jordan Elimination and check using Cramer's Rule. x1+5x2-x3=74x1+3x2+6x3=15