2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly independent on the interval (-x, 0). %3D

Q: y"-uy'+5y= e Sin() %3D

A: We have to solve given problem:

Q: Find the differential dy of the given function.

A: Given :              The given function is :                   y = 9 - x2 To find :            The…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: Given function f(x)=mx+b where m and b is constant our aim To evaluate linearization of f(x) at…

Q: Find the differential dy of the given function.     y = 3x2/3

A:

Q: Find the general solutions to the given differential eguations y" – 2y' + y = x² – 1

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A: Given family of Curve is x2-3xy-2y2=C

Q: find a linear differential operator that annihilates the given function. y = x sin(3x)+ 3xe6x

A:

Q: (1) Use the linear approximation of Va at x = 9 to estimate the value of v8.7

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx +b at any given…

A: Givenf(x)=mx +b where m and b are constantsTo find linearization of f.

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

A:

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

A:

Q: Find the differential of the given functions: 1. y = 3x4 - 5x³ + x - 4 2. u = /2y – y3

A:

Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

A:

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: 4) Consider the function 9 defined by g(x, y) = cas (7X Jj ) + logg(x-y) does 9 ha ve the maximum…

A: direction of maximum increase  Let maximum rate of change of a function f(x,y)  occur in the…

Q: х+1 y = 2x

A:

Q: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

A:

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

A:

Q: 1 A point is moving along the graph of the functiony = dy 9x2 + 6 such that dt = 3 centimeters per…

A:

Q: v = ) V In(2x-3y

A:

Q: x³y³dy у2— 4у-21 (x – x4y)dy + (y + x³y²)dx :

A: See the solution and follow the step.

Q: Solve the Ro liowing B E 2 X + 2 -zey= zX

A:

Q: Let y = 4x“. Find the change in y, Ay when x = 3 and Ax Find the differential dy when x = 3 and dæ =…

A: Given that: y=4x2, x=3 and ∆x=0.4

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: S(«,9) =7+3y Also, find the total differential of the function.

A:

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A:

Q: Find the differential dy of the given function. y = √√√√9-x²

A: Given y=9-x2 we need to find dy

Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A:

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ ( 1. (D³ - 5D² + 3D + 9)y = 0 2. (D³ - D² –…

A:

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: The given function is: f(x)=mx+bSo,f'(x)=m

Q: 8. Find the orthogonal trajectories of y = cx CX

A:

Q: Find a linear differential operator (of lowest order) that annihilates the given function: f (x) =…

A:

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: 2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

A: Given that: cos(wt-B), coswt, sinwt

Q: 1. Find the orthogonal trajectories of the family of curve z² + 3y which is passing through (10,…

A:

Q: Find the number N such that the differential (y^3-2x)dx+Nxy^2dy is exact

A:

Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). * y = In(e* + e4r) 2y +…

A:

Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: 1. Construct a slope field for the differential dy = x + 2y dx equation

A:

Q: If C, and C, are constant vectors and A is a constant scalar, show that H - e* (C1 sin Ày +C2 cos…

A:

Q: (a) Consider the direction field of the differential equation dy/dx = x(y – 8)2 - 4, but do not use…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Find the differential dy of the given function.    y = x√(1 − x2)

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

A:

Q: 8. Find the orthogonal trajectories of y cx

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.