Which of the following is true for the equation 5 - 3 (2r – 7) = 2 (7 – 3æ)? %3D AT=0 B)x = 28 CThe equation has no solution. D The equation has infinitely many solutions.

Q: - for the 2 equations, a,X+a12Xg=0 and aX,+aNg=2 the value of au given: and a11 a121 la21 a221 X= 1,…

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Q: 3. Find the values of m such that y =e is a solution of the following equations a) 3y"-5y'= 0,

A: The given differential equation is                                                        3y''-5y'=0…

Q: Solve the given DE using 3 possible solutions: y' X 3 - 2y 3 3xy 2

A: Given DE  y'=x3-2y33xy2  …………………………(i) we can write it as dydx=x3-2y33xy2

Q: The general solution to D. E 2y(4) – y'"" – 2y" + y' = 0 - is given by y(x) =

A: The genaral solution to D.E2y(4)-y'''-2y''+y'=0

Q: Which of the following is a solution to xy' + y + x*y*e* = 0 ? y3 = x³(3e* + x) y3 = x³(3e* + C) %3D…

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Q: Given that y = et is a solution to the equation ty" – (t + 1)y' + y = = 0, - which of the following…

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Q: 1. Solve for x: 5(х — 1) — -35 2. Solve for t: -3(2t + 35) = 9 %3D 3.4(v – 1) = w 3. In the equation…

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Q: Consider the following equation + 2r –n(n+1)C =0 Assume a solution of the form C=r and solve for A…

A: Given that : r2∂2c∂r2+2r∂c∂r-n(n+1)C=0If c =rλ,r2∂2rλ∂r2+2r∂rλ∂r-n(n+1)rλ=0It is in the form of…

Q: IV. Do the following as indicated a) Give a particular solution for y" – 2y' + y = 3e*. b) Give a…

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Q: Q2. If the solution of the below first order D.E is y = C ef(x,y) (x³ + xy²)y' = y3 Find the f(x,y).

A: x3+xy2y' = y3dydx=y3x3+xy2 ........................equation(1)Let put y = vx in equation(1) and…

Q: The solution of the DE (4xy -3)y' =-2y² -1 is 2xy² + x – 3y = c O None of these 2хy? - х - Зу 3 с…

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Q: Q2. If the solution of the below first order D.E is y = C ef(x.y) (x³ + xy²)y' = y3 Find the f(x,…

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Q: Which of the following is a general solution to the DE y =3x² +5? A y=x³+C B y=3x²+ C (c) y=6x+ C…

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Q: Which of the following is not a solution to d'y dr2 4y +1

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Q: Which of the following is a solution to y" – 6x = 2? a. y = x3 b. y = x c. y = x3 + x? с. d. All of…

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Q: e lab, Alonzo has two solutions that contain alcohol and is mixing them with each other. Solution A…

A: Please refer to the image below

Q: 4. Verify whether the following equation is exact. If possible, solve the equation. a) (2.re +u +…

A: on solving these diffrential equation we will get

Q: 5. (D² + 4D + 4)y = 0 ;when x = 0,y = 1,y' = -1

A: Given equation is, D2+4D+4y=0, x=0, y=1, y'=-1 Now, write the auxiliary equation for the given…

Q: 3. Find the values of m such that y=e is a solution of the following equations a) 3y"-5y'=0,

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Q: with the understanding that D = find a complete solution of the following: (2D + 1)x + (D + 1)y = 3

A: Given that…

Q: 1. Solve (D? + D;)z = 0 2. Solve (D– 2D,D, + 5D)z = 0 %3D y

A: 1) Given partial differential equation is: (Dx2+Dy2)z=0 Write auxiliary equation corresponding to…

Q: Solve the following equations for x. (a) 3e2 5e" + 2 3e2" = (3a – 1)e² + a, where a is a constant.…

A: The objective is to solve the equation for x.

Q: 1.4 Solve the following equations for r. | 3e²* = 5e* +2 3e2 = (3a – 1)e² +a, where a is a constant.…

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Q: 3. Find the general solution of + - 3x?y? А. 1/(ху) %3D -з(*/2) + с В. 1/(ху) %3D -З(x/2) + с с.…

A: Here in starting it is bernouli form so taking v=y1-n and solving and reducing it to y'+…

Q: Solve the following simultaneous linear D.E. 1 6 [²D+ ₁ D + ¹])} = {e} 7 }{}

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Q: Q5. In the given problems determine whether the given equation is exact. If exact solve. (х + у)(х —…

A: Please refer the attached image for complete solution.

Q: The general solution of the following : O.D.E is y(4) – 2 y(3) + 3 y(2) = 0

A:

Q: ds 13. dt 1 s tan = CSC -- | 2 2 2

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: The value of k so that (y³ +kxy* – 2x)dx + (3xy? +20x?y³ )dy = 0is an exact equa is: а. 10 С. -5 b.…

A: A differential equation of the form Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x

Q: (x*+ 2y)dx — хdу y' = csc x – ycot x

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Q: There is a solution z e C to the equation + 2 = 0. Select one: OTrue OFalse

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Q: 1. Solve the following equations for x. (a) 3e2x = 5e* + 2 (b) 3e2* = (3a - 1) e* + a, where a is a…

A: Exponential equation

Q: Find the general equation of the following DE: 4. (D3 − D2 + D − 1)y = 4sinx

A: Given: (D3 − D2 + D − 1)y = 4sinx

Q: 29. Solve the equation for the indicated variable. D= 3ef, for e Oe = = Oe = D-(3/) Oe= 35 -D D-3 2.

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Q: Find the general solution of the following 1. (D² – D – 2)y = 0 %3D

A: To find- Find the general solution of the following: D2 - D - 2y = 0

Q: The appropriate form of the particular solution for y"-9y r+e3 is: Select one: Yp = Ar + B+ Cez %3D…

A: In this question we have to find appropriate form of particular solution given in the question.

Q: For which value of b is the equation 2n+1 3n 19 satisfied, 4 4n+1 n= 1 where b>2 ?

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Q: The roots of the auxiliary equation of a DE are: m 3, 3, 3 t 3i.Then solution of the equation is,

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Q: d²y #3. Find if x' + y' = 9 dx? |(-1,2)

A: x2 + y3  =9 now differentiate it  2x + 3y2(dy/dx) = 0 dy/dx = -2x/3y2 now agian differentiate with x…

Q: g'ay-3y=(2tが)et

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Q: d?y +4 dr? 4. Find the general solution to + 3y = e- dr

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Q: 2y" — 12" + 4у' + 72у %3D 0

A: Given ode is homogenous. We will find root of this ode then we write solution.

Q: Find the particular solution to the following equation y" + 4y' + 5y = 0 y(0) = 1; y'(0) = -3 Hint:…

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Q: Find the Solution (1+r?)ds + 21[st²– 3(1+1²)²]dt = 0; when 1 = 0, s = 2. = (1+ s?)13-e-

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Q: For what value of k the linear Diophantine equation 21x + 14y k has solution k = 1 b) k = 36 e) k=…

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Q: Given that y = et is a solution to the equation ty" – (t + 1)y + y = = 0, which of the following is…

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Q: Which of the following is the general solution of the separable equation, dy/dx = 12x³y? A. y =…

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Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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Q: Solve for the unknown using principles of equations: а. бх + 8 — За 3D — 8а — 10 + х 0.00 Rounded to…

A: Solution a: 6x+8-3x=-8x-10+x⇒6x-3x+8x-x=-10-8⇒(6-3+8-1)x=-18⇒10x=-18 Now divide both side by 10…

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.