Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a have a unique solution.

Q: Show that the equations x+ y +z = 4, 2x + 5y - 2z = 3, x + 7y - 7z = 5 are not consistent.

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Q: Give the general solution to the equation x' Ax where A = %3D

A: To find the general solution of the given system, first we find the eigenvalues and corresponding…

Q: Find the number of non negative solutions to x+y+z= 21. With the conditions that x < 3, y ≥ 2, z ≥…

A: Given that x+y+z=21 with the conditions x&lt;3, y≥2, z≥4

Q: Find the solution of the equation on the interval [0, 2π).

A: We have, cos (A+B) = cos A cos B - sin A sin B sin (A-B) = sin A cos B-cos A sin B

Q: For the equation Mdx+Ndy=0, if both M and N follows that f(Ax,\y)=^k f(x,y), the equation is A.…

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Q: Find two linearly independent solutions to x2y′′+x(3−2x)y′+(1−2x)y =0 on (0,∞).

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Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: 14. If f(z) = 2 + z² – zª, then the equation S(x) = 0has a solution on the interval A [1,2] B (0,1]…

A: We will make use of the fact that for f to have a solution in an interval it must be that f has…

Q: y = xe * satisfies the equation ry' = (1 – x²) y. %3D

A: Given differential equation  xy'=1-x2y

Q: Solve the DE y'=(x+y+2)^2, y(0)=2 by setting u=x+y+2.

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Q: Solve by reduction of order. Find y2 and y (x² + 1)y" – 2xy' + 2y = 0 yı = x -

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Q: Give a particular solution for y" – 2y' + y = 3e*.

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Q: 14. If f(z) = 2 + ² -r', then the equation S(z) = 0has a solution on the interval A [1,2] B (0,1] c…

A: Given equation, fx=2+x2-x3, To find the interval on which the equation fx=0 has a solution.

Q: Find two linearly independent solutions of 2x2y"-xy'+(-6x+1)y=0, x>0 of the form

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: find the explicit solution of y' +xy = x√ y

A: This is a basic differential equation problem

Q: For which values of the constant c is a linear -日 combination of a and where a and b are 62…

A: We have to find values of c

Q: Show that the equation x+y+z=4,2x+5y-2z=3,x+7y-7z=5 are not constant

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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: (e) f(x1,x2) = xỉ/x2 on R x R++.

A: The solution of (e) is in below

Q: 3. Which equation passes through the point (1, -2) and is perpendicular to y = x O y = 3x - 1 O y =…

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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: y(4) + 3y" + 2Y = 0

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Q: Find the particular solution of r*y – y y+1 ; y (3) = -1

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Q: Y= (10x; + x, } (5x, + x}} 15

A: We have to differentiate partially to this equation:

Q: . Verify directly that y = 12 + Ce−3t satisfies y = −3(y − 12)forall C. Then find the two solutions…

A: Given :                 The general solution of y' = -3y(y-12) is                            y =…

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: Find the particular solution for ysqrt(1-x^2) * y'-xsqrt(1-y^2)=0  when y(0)=1

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Q: We have found that the roots of the auxiliary equation are m, = -1 and m, = -2. In the case that the…

A: We have to find wronskian .

Q: Eliminate the arbitrary constants of  y=e^(-3x) (Acos5x - Bsin5x) + Cx Where A, B,  and C are the…

A: It is given that, y=e-3x(Acos5x-Bsin5x)+Cx. Obtain the first derivative as follows:…

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

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Q: Find the equation of a line perpendicular to 3x – 2y = 16 that passes through the point (9, 4). - Oy…

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Q: solution for z(x, 0) = x², z(1,)

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Q: 2: Show that the line equation passing through two distinct points (a1, b1) and (a2, b2) can be…

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Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: Find the initial value of the relation y = 3(x+3)² + 7

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Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: Find two linearly independent solutions of the equation (x-1)y"+y=O for |x|<1

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Q: 2xy y' + 2x² x' = y² x'

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

Q: The equation below is said to be A. Linear in x O B. Linear in y C. Linear in both x and y O D.…

A: We will find out the required value.

Q: Find Solution AUP : gruen xlo)=2 4 %3D - -3

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Q: let y"(x) + y(x) = 0 be given What would be a suitable solution y(x)?

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Q: What points (x, y, z) satisfy the equations x2 + y2 = 4 and z = 3?

A: Given: x2+y2=4, z=3

Q: Consider the following system of equations in R²→R? y + 2xỉ + x3 - yıY2 = 15 2y + xỉ + x + YıY2 = 38…

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Q: b- Find the solution of f(x) e-x, let x, 0 and E- 10-5

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Q: Give a particular solution for y" – 2y' + y = 3e*

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Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…

Q: 2. Find the solution set of the following linear equations. (а) х — 2у — z%3D —2 - - (b) 3x – 7y =…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.