If the auxiliary roots of a certain HLDE with constant coefficients are 2, -3, and -3, then the general solution is A y=c,e¯+c B y=c,e+c 3x -3x +c,xe y=c,e-+c 3x O y=c,e"+c,e -3x Cze +c

Q: If roots of x³ + 5x² – 7x – 1 = 0 are a, B, Y then the equation whose roots are aß, By, Ya is- (1)…

A: To find the cubic equation with the roots as aB , Br and ra

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: Is (2, –1, 3) a solution of 3x + 5y – 2z = -5 2х + Зу- z 3D —2 2x + 4y + 6z 18? Replace x with 2, y…

A: Consider the system of equations. 3x+5y-2z=-52x+3y-z=-22x+4y+6z=18 And, the solution of the system…

Q: Find a quadratic equation whose product of roots x, and x₂ is X₂ equal to 4 and satisfying the…

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Q: GIVEN: (xn , yn) = (1, 3), (2, 4), (4, 7), (5, 9) Determine the best-fit quadratic curve that…

A: GIVEN: (xn, yn)=(1, 3), (2, 4), (4, 7), (5, 9) we have to determine best-fit quadratic curve that…

Q: If the auxiliary roots of a certain HLDE with constant coefficients are 0, -1, and 3, then the…

A: Solution is given as below:

Q: The linear Diophantine equation ах + бу — С = c has a solution if, and only if,

A: The linear diophantine equation is in the form, ax+by=c,

Q: would you prove that the answers to the diophantine equation y^2-x^3=0 are the pairs (n^2,n^3) for…

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Q: 7. Determine the roots of y4 + y"" −y" -y+1=0 a. 1,-1,1 b. 1-1,-1 c. 1,-1,2 d. 1,-1, -2

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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: 10. Write the sustem of lineor equations in the form Arebuand solve this motrit equat 2と, X, t Xu-9…

A: Given: 2x1  -x2 +x4 =93x2 -x3 -x4 =-9x1 +x3 -3x4 =-2x1 +x2 +2x3 =0 To find : x1x2x3x4 for system of…

Q: If 7, r, and r, are the roots of equation x-2x+3=0, then findErr,. إختر أحد الخيارات: -2 a O .b O…

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Q: Let x, y be the unique solution of x' = y y' = 0, y(0) = 1. = -x x (0) Show that x, y verify x2 + y?…

A: Given x' = y                   (1)y' = -x                (2)x(0) = 0                    (3)y(0) = 1…

Q: A solution of a DE which is not exact and falls under Case 3 i.e. a2 can alone be solved by b2 DE…

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Q: Which of the following equations can be reduced to be a separable equation?

A: I.  2xy-tanydx+x2-xsec2ydy=0 ⇒ 2xy.dx+x2dy-tany.dx-xsec2y.dy=0⇒dx2y-dx.tany=0  Integrate both…

Q: If the auxiliary roots of a certain HLDE with constant coefficients are 0. -1, and 3, then the…

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Q: If the roots of equation x² - 2cx + ab = 0 a the that th of 2 20 41

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Q: Write down all of the product solutions satisfying: и +иу —D 0, 0 <x<2, 0<у<1. %3D u(х,0) — 0, и,…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Find an equation whose roots are the 3 times the reciprocal of the roots of 6x-4x +3x-4 0. 6y' -4y?…

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Q: Show that a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of the…

A: To show that  a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of…

Q: Using Cramer's rule to solve Зх + у + 42 - 2х + Зу - 2z x - 3y – 27 = -8 %3D 11 %3D 4 for y, we…

A: Consider the given information. 3x+y+4z=-82x+3y-2z=11x-3y-2z=4 Now, make the matrix D, according to…

Q: 1. Determine the nature of the roots of the following equations: (a) 3x + 5x +4 = 0 (c) x-8x + 16 =…

A: Given that: 1x-1x+1=15

Q: (4) Show that in general, the sum of the roots of a quadratic equation ax2 + bx + c = 0 is --…

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Q: Given that 3+2i is a root of the equation x^4-8x^3+30x^2-56x+65=0.Which of the following quadratic…

A: Given: 3+2i  is a root of the equation:  x4-8x3+30x2-56x+65=0

Q: Use the four roots of the equation z'+4 = 0: w, = 1+i, w, = -1+i, w, = -1- i, w, =1-i, to factor…

A: Given equation is z4+4=0 find the roots of the equation

Q: Find the solution of the given ODE. (6x² - 7y2) dx - 14xydy = 0 2x³ - 7xy² = C 3x² - 14xy² = C O…

A: Given problem:- Find the solution of the given ODE.   (6x2 - 7y2) dx - 14xydy = 0

Q: To prove the equation r + z –1=0 has exactly one real root, %3D

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Q: (4) Show that in general the sum of the roots of a quadratic equation ax? + bx +e=0 b is --whereas…

A: Let u and v be the roots of a quadratic equation ax2+bx+c=0. To obtain the equation from the roots,…

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.

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Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that w=5…

A: If we have an equation of the form x⩾a then the variable x can take up any value greater than or…

Q: utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1

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Q: 1. Use the graph of y = VI to estimate the solution(s) to the following equations YA -150 -120 -90…

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

Q: 2xy y' + 2x² x' = y² x'

A: Given: 2xyy' + 2x3x' = y2x' ⇒2xydy + 2x3dx = y2dx ⇒2xydy- y2dx=- 2x3dx

Q: 1. What are the roots of the equation (x + 1)(4x – 3) = 0? C) x= 1, - D) x= 1 A) x = -1,3 B) x= -1,

A: (x+1)(4x-3)=0⇒(x+1)=0 or (4x-3)=0⇒x=-1 or 4x=3⇒x=-1 or x=34⇒x=-1 ,34

Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, then prove that the roots of x²…

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Q: Let A and B be real numbers such that a root of the equation z ^ 3 + Az ^ 2 + Bz + 26 = 0 is 1 + i.…

A: First of all, as coefficients A and B are real, we know that, if z ∈ C is a root of an equation,…

Q: 8. Which of the following are approximate roots of the equation -óx? + 20 = 43x? a x--7.61, 0.44 c…

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Q: 4. Which of the qundratic equation has no real roots? 1. x*+ 3x - 10 -0 5 Whnt is the nature of…

A: The equation ax2 +bx+c= 0 has real roots if b2 -4ac=0

Q: If a, b, c are in GP and the equation ax² +2bx+c= 0 and dx² +2ex+f=0 have a common root, then is it…

A: Given that a,b,c in G.P and the equation ax2+2bx+c=0 and dx2+2ex+f=0 have a common root.

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: If the auxiliary roots of a certain HLDE with constant coefficients are 0. -1, and 3, then the…

A:

Q: Find all solutions in positive integers of the diophantine equation x^2 + 3y^2 = z^2

A: Given: A diophantine equation x2+3y2=z2 To find: x,y,z/x,y,z∈ℤ+

Q: The substitution 1/2(1 – *k) Yk = (6.106) transforms the equation Yk+1 = 2у. (1 — ук) (6.107) into (…

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

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Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--