9. Prove that 0 has The equation x+ ax+ b2 one (a) negative and two imaginary roots if b 0. TL

Q: 3. Solve the particular solution (D² + 3D + 5)y = 5e¬*sin2x using D- operator method.

A:

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: у" - у' - 2sin 2x

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Q: 5. Find a general solution to the Cauchy-Euler equation x?y" + 7xy' + 9y = 0, for x > 0.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

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: Q.4 Solve Cauchy Euler DE x³y" + 4x²y" – 5xy' – 15y = x*

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Q: 2. Find general solution of the DE y" + 3y" + 3/ + y = 0

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Q: П. Solve xау + (3х 2y)ax = U in two ways

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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…

A:

Q: 1.Find the roots of the equation f(x) = x³ - x - 1 using xo 1 %3D %3D For 4 iteration by fixed…

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Q: Find the wrong Kian W(y1,y2)(t) of y1 and y2  Where y1=t and y2= e^t are solutions of…

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Q: Find the general solution of i = Ax, where A = .

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Q: 1. Eliminate the arbitrary constants on the given equation: y = C1 + C2e¯ -2x 2 Eliminato

A: Given

Q: determine the second approximation Xz if Ne wtons Method was use to defermine the root o f the…

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Q: A quadratic equation x^2- 4x+4=O is defined with an initial guess of x(0)=3 and x(1)=2.5. Find the…

A: The complete solutions are given below

Q: 19. Show that yı = 1 and y2 = /x are solutions of yy" + (y')² = 0, but that their sum y = y1 + y2 is…

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Q: 14.Show that any separable equation M(x)+N(y)y′=0 is also exact.

A: Given: Mx+Nyy'=0

Q: 1. The initial guesses of the roots are x-1 = 2.5 and x, = 3.5 , what is the next iterative value of…

A: According to our company guidelines, we can solve the first question only and the rest can be…

Q: Prove that the following equation has no natural solutions x? + x +1 = y².

A: we have to prove that given equation has no natural solution

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: Solve the following Higher Order Non-homogenous DE using Methods of undetermined coefficients…

A: Given,y'' -2y' +y=3x+2A second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y- C

A:

Q: 4) To find the root of the equation x² - 3 = 0 using the fixed point method in [1,2], one of the…

A: The given problem is to find the iteration formula for finding the root of the given equation x2-3=0…

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: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

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Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: 1d. Show that the given equation x- In xX= 0, has a root in the interval [4, 5].

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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: show that the Pio Diophant ine equation 2x -5y= | has no integer Selutions .

A: Given, 2x²=1+5y² Here 5y2 is a multiple of 5 ending in digit 5 or 0. 2x2 can end in 1 or 6 But no…

Q: Find the general solution of (3D2 + 5DD' - 2D'2)Z = 10 cosh(2x + 5y).

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: 4. Solve the equation T2T satisfying the conditions: at ax (i) T=0 when x= 0 and 1 for all t 2x,…

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

Q: Use variation of parameters to find yp of x²y" - 2xy' + 2 y = -12 x(1/2) given that yi = x and y2 x2…

A:

Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

A:

Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

Q: 4) To find the root of the equation x²-3 = 0 using the fixed point method in [1,2], one of the…

A:

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: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

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Q: 2. u(z) +

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Q: 2. Use the Newton-Raphson method to find a root of the equation x - 2x - 5 = 0 and an %3D initial…

A: 2. Given equation is f(x)= x3-2x-5 f'(x)=3x2-2 x0=0 First Iteration:  First iteration:…

Q: Find the first approximation to the root of the equation x - 2x - 5 = 0 using Regular-Falsi method…

A:

Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

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

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Q: 4) To find the root of the equation x² - 6 -0 by using the fixed point method in [1,21 one of the…

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Q: Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the…

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Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

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Q: 4. Find the solution to the IVP in explicit form and determine the interval in which the solution is…

A: y'=3x2-ex2y-5dydx=3x2-ex2y-5(2y-5)dy=3x2-exdx Integrate both sides