Find fy, fy, fz- f(x.y.z) = 4x – /3y²+z? f = (Type an exact answer, using radicals as needed.) (Type an exact answer, using radicals as needed.) f, = (Type an exact answer, using radicals as needed.)

Q: find the seril solution of the equation y``+  4xy = 0  at the neighborhood of the  point  x0 = 0

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Q: Find all integral solutions of the linear Diophantine equations 6x + 11y = 41

A: We recall a standard theorem about Linear Diophantine Equation and then use that theorem to solve…

Q: Find the positive root of the equation xe^x-3 using regula falsi method and correct to 4 decimal…

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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: Let P(z) = z100 + 8z10 – 3z³ + z² + z + 1. Find the number of roots of P(z) (solutions of the…

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Q: Find the general solution of y " - 7y " + 16y' – 12y =0 given that r = 3 is a root of the…

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Q: (x² + 4xy + 2y²)dy + xydx = 0

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Q: Obtain the general solution valid near the origin: 2y" + 9xy' − 36y = 0

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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: Find a general solution of the equation: 5xy' = 2 – y %3D

A: Please find attachment for the details solution

Q: af ay f(x,y)=√√4x²+ +y² af Find and əx || (Type an exact answer, using radicals as needed.)

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Q: If f(x) = 0 is a cubic equation whose roots are a, B, y and a is the harmonic mean of the roois %3D…

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Q: Find all the roots of f (z) = 2z% + 81/3 – j81 |3D

A: Introduction: A complex number includes the imaginary number i=-1. Due to the presence of this…

Q: B) The roots of HX-3X + 2 =o are a and B. Snd s Land x+P equation whose roots Mew are

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Q: Find fx, fy, f₂. fx = f(x,y,z)=x-√√√²+z² (Type an exact answer, using radicals as needed.)

A: The given function is fx,y,x=x-y2+z2. We have to find fx,fy and fz.

Q: dy 24. Find dr? in terms of x and y. 6-8xy 9x-5y %3D

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Q: B) Find the approximate roots of the following equation: f (x) = x³ – 8 = 0, on the closed interval…

A: Use the bisection method to find the roots of x3-8=0 find two points such that f(a)fb<0…

Q: The indicial equation of (-1) y"+ (-1)y'+2u 0 at r=1 is: (A) + 2r +1=0 (B) r1 2r = 0 (C) r-r= 0 (D)…

A: Given differential equation is (x-1)2y"+(x3-1)y'+2y = 0

Q: Find two fundamental solutions x²y" + 4xy' + (2+x)y= 0,

A: We have to solve given problem:

Q: Determine for which values of m the function 4(x) = x"' is a solution to the given equation. d´y dy…

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Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

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Q: Obtain the GS of: 2 (Згу — 4у + 6) dz + (23 — ва? ? — 1) dy %3D 0 - a. x³y – 2x?y3 + 3x² b. x3у —…

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Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

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Q: * Find grad A at p (1, -1, 1) for A = 3x² y z %3D - 6 i+ 3j-3k O 6 i +3j+ 3k O - 6i O -3 O Simplify…

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Q: x²y" – 5xy'+9y = 2x

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

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Q: Show that the general cubic equation y3 + by2 + cy + d = 0can be transformed into an equation of the…

A: To find the equation of the form

Q: C. Solve the following using Intearating Factor by Formulas. 2. у(2х — у + 1)ах + x(3х — 4у + 3)dy…

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Q: Choose the suitable substitution for the method of reduction of order to find a second solution y2…

A: Given differential equation is y'' + 11y' + 18y = 0

Q: 18. Determine the roots of the auxiliary equation of y" + 3y" – 4y – 12y =

A: Follow the procedure given below.

Q: 1. For each of the following quadratic equations, determine the number and the nature of the roots…

A: We have, 1. x2+8x+11=02. 4x2+4x-7=0   General quadratic equation is defined as, ax2+bx+c=0 Here…

Q: Find fy, fy, fz- 2 2 f(x,y,z) = 4x - Vy + 4z (Type an exact answer, using radicals as needed.)

A: We have to solve

Q: , obtain a formula for the local truncation error for the Euler method in terms of t and the exact…

A: Consider the given initial value problem y′=√(t+y), y(1)=3.

Q: Find the real roots of y''' + y = 0 with constant coefficients

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Q: Find the second approximation to the root of the equation x–4x-9=0using bisection method, if a,…

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Q: Find fx. fy, f₂. 2 2 f(x,y,z) = 3x -√√4y +z² fx= 3 (Type an exact answer, using radicals as needed.)…

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Q: Solve z+z +1= 0 by obtaining the roots. Answer a. b(1+jv3), }(-1± N) 幸 d. (1+ jv/3), (-1±jv3)

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Q: use the methor of undetermined coefficients to find the gen. sol to: y'' - 3y' +2y = t2 + 2 e-t

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Q: Solve the DE by Method of Undetermined Coefficients iv y" +5y +4y = 90 sin 4x %3D y (0) = 1, y (0) =…

A: The given initial value problem is: y''''+5y''+4y=90 sin(4x);          y(0)=1, y'(0)=2, y''(0)=-1,…

Q: Use the Runge-Kutta method to solve the equation y" = xy' +y for x= 0-0(0-2)2-0 given that at x = 0,…

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Q: ind the roots of the linear equations using Crout's Method 5X1 + 4X2 + X3 = 3.4 10X1 + 9X2 +…

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Q: of of and Find dy f(x.y) = Vx + 5y² O Type an exact answer, using radicals as needed.) of (Type an…

A: →During calculation of ∂f(x,y)∂x , consider y as constant.→ During calculation of ∂f(x,y)∂y ,…

Q: Make a change of variable, x =Py, that transforms the given quadratic form into a quadratic form…

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Q: Find general solution of the DE 4x2y′′ + 8xy′ + y = 0

A: Consider the given equation. 4x2y''+8xy'+y=0 Let substitute the value is y=xm. Now, find the…

Q: If a tank holds 8000 gallons of water, which drains from the bottom of the tank in 40 minutes, then…

A: Given: The capacity of tanks 8000 gallons. V=80001-t402

Q: Find the change of variable x = Py that transforms the quadratic form x'Ax into y' Dy as shown…

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

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Q: Find the solution of the given syst- x+3y +3z=2 x+4y +3z=3 x+3y +4z =1

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Q: Use the method of reduction of order to find a second solution to t'y" + 2ty' – 2y = 0, t>0 Given y1…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.