9. Which of the following equations matches standard form of a quadratic ax + by = c y = a(x-h)² + k y = ax2 + bx + C

Q: 2) [3 Solve the IVP: y" - 6y + 8y = 0, y(0) = 0, y' (0) = 2.

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Q: 2. Eliminate the arbitrary constants a and b from the following equations to form the PDE: (a) ax? +…

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Q: (a) Solve the following linear equation by Cramar's rule:- x- y + 2z = -4 3x + y - 4z = -6 2x + 3y -…

A: a Given system of linear equation is x−y+2z=−43x+y−4z=−62x+3y−4z=4 Here, A|b=1−12−431−4−623−44 Here,…

Q: 7. If the quadratic equation x² + (k – 2)x – 2k = 0 has real and equal roots then A (k– 2)² = 0 B (k…

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Q: 7. Prove (by writing the linear algebraic equations explicitly) that (a) If x-y=0, then =ỷ where X,ỷ…

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Q: 5) Find a general solution of the equation y" - 7y' +6y=3e³x. 11 - 7y! + by = 365x - Ar + 6 = 3e³z…

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Q: 3. Prove that the solution to the equation 9yy + 4x = 0 can also be written as: y2 = c: and what is…

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Q: 4. As an engineer and a scientist, a research has been conducted and the problem has been modeled…

A: We will find out the required maximum value for given objective function.

Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: Determine whether y, = 3e2t – e-3t and yz = 2e-3t – 6e2t form a fundamental set of solutions. HOW…

A: We have to determine whether the given set of solutions y1 and y2 form a  fundamental set of…

Q: 2. Determine the complete solution of xydy – (x + 2y)²dy = 0 %3D

A:

Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

Q: الوضوع Solve by simplex method the following.Linear prablem : Max Z= 2 Xx +3 Xz stabject to: - 1) X,…

A:

Q: ,solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.

A: To Determine: solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.…

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: (9) Does the equation r2 - 31y² = -45 have a solution? %3D in itegers please

A: The set of all (x,y) that satisfy an equation, y=f(x) are the solution of the equation.

Q: Let (x, Y,) be the solution of the following equations (2x)" = (3y)m3 3Inx = 2lny In 2 %3| %3D Then…

A: Introduction :

Q: 1. Use the simplex method to solve the following problem. Also verify your an using the dual of the…

A: We are not allowed to give handwritten solutions unless and until the question is too complex to…

Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

A:

Q: 10. Find the particular solution that satisfies the initial condition. my'+2y = 3x2-5x, Initial…

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Q: 4. Find the number of non negative solutions to x + y + z = 21. With the conditions that x > 3, y >…

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Q: Show that the equation 3x+4y+5z=a, 4x+5y+6z=b and 5x+6y+7z=0 do not have a solution unless a+c=2b

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Q: Find the optimal solution. MAX Z=6X+7Y st 4X+5Y≤20 10X+7Y≤35 3X+4Y≥6 X ≥0 , Y ≥0 and an…

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Q: You know that an equation has zeros at –2, 0, 1, 4 and also that x-∞, y--∞. Which of the following…

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Q: 4. Obtain the general solution (D + D - 9D - Dy = 6e - X 3x + 3xe

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Q: What is the general solution of xy^2dx+x^2ydy=0

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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: (a) Solve the following linear equation by Cramar's rule:- x- y + 2z = –-4 3x + y – 4z = -6 2x + 3y…

A:

Q: Show that the equation 2³ + 3y3 = 923 has no solution in integers, other than x = y = z = 0.

A: Suppose that, x3+3y3=9z2 has a non-trivial solution, that is other than (0,0,0), and minimal.

Q: 6. Use undetermined coefficients to find a general solution of -2x y" + 5y' + 6y = 3e¬2= +e3z

A: The given differential equation is y''+5y'+6y=3e-2x+e3x

Q: 1. Find the number of non negative solutions to x + y + z + w 16. With the conditions that x > 2, y…

A: The complete solutions are given below

Q: 8. Find the particular solution of x²y"+ xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: eular method

Q: 2. Obtain the solution set of z* - j3z² – 2 = 0. (Hint: factoring and quadratic formula)

A:

Q: determine by inspection at least two solutions of the given first-order IV . 15. y-  3y2/3, y(0) …

A: Consider the given y'=3y23 and y0=0

Q: 1. Show that y = c,x1 + c,x³ is a family of solutions of x?y" - xy' - 3y = 0.

A:

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

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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 & lengthy problem.So I can do it in Advanced Mathematics.

Q: Verify that y = c1x+c2Vx+ is the general solution of the 6x following nonhomogeneous 2.²y" – xy' + y…

A: Derivative of xn: Derivative of an exponential function that is, xn is given by the formula,…

Q: 2x (융) 1 y: x'; yel, X-1

A: Consider the given equation as x+6ydx-2xdy=0

Q: y" + 10y' + 26y =0

A:

Q: Provide general solution of the given ay'' + by' + cy = 0and b^2 - 4ac < 0

A: Solution: Consider the given differential equation is ay'' + by' + c y = 0 or aD2+bD+cy = 0   where…

Q: Consider the following LP Min z = 3x, + 2.x, + 7x, s.t =10 r+ 'r - -2x, + x, – x, <-10 %3D In…

A: Max Z =   3 x1 + 2 x2 + 7 x3 subject to -   x1 +   x2       = 10 - 2 x1 +   x2 -   x3…

Q: 4. Which of these stnadard form equations is equivalent to (x+ 1)(x-2)(x+4) (3x+7)? O x* + 10x +…

A: value=?

Q: 2.40 Solve the following problem for x (t) and y(t): x = -2x + 5y y = -6y - 4x + 10us (1) x(0)=5…

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Q: b) Find particular solution of х*у 3- (х-1) у. У(1) — 1. У(1) %3D 1.

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

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Q: Find the general solution. 6y(4) + 7y" – 12y" – 3y' + 2y = 0 SHOW WORK.

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Q: Verify that yp = 3e2x is a particular solutions of y" − 6y′ + 5? = −9e2x .

A: Explanation is given below...

Q: 10. Find the particular solution that satisfies the initial condition. xy'+ 2y = 3x² – 5x. Initial…

A: