Consider the function f(x) = 5x10 + 9x° – 3x³ – 8. An antiderivative of f(x) is F(x) = Ax" + Bx" + CxP + Dxª where 6 %3D A is and n is and B is and m is and C is and p is and D is and q is

Q: If f(x, y) = 4e*y cos (x- 1) , then the linear approximation at (1,0) is | (A) 4 + 16x (B) 4 + 4x…

A:

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: Find the general antiderivative of f(x) = + C - 5x¹ x² +6√x

A:

Q: Find the particular solution of y2dx+x(x+y)dy=0, when x=1, y=1. Let x=vy.

A:

Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: In each exercise, obtain the particular of solution. a. (y + Vx2 + y²) dx – x dy = 0; when x = V3, y…

A:

Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

Q: a. Find the antiderivative of f(x) = -25x e F(x) = %3D

A:

Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

A:

Q: 1. Answer the following questions: (a) Find the linear approximation of y- f(x)-Vr at a 256 and (b)…

A: Firstly, we will calculate f'(x), then f(a), f'(a).

Q: The y, of y'"-y=2x2-x -3 by using variation of parameters is: .A Y,(x)= x - 1 .B y,(x)=x² + x +1 .C…

A:

Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

A:

Q: c) Find the second degree polynomial approximation to f at (a, b) = (1, – 2) T2(x, y)

A: Given :- The second degree polynomial approximation to f at a,b = 1,-2 f x,y = -x2y2x2 +y2

Q: Consider the function f(x) = 31°+ 9x' 10r° – 7. | An antiderivative of f(x) is F(x) = Ar" + Bæ™ +…

A:

Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1 O a. y (2y-3x) = 3x? O…

A:

Q: 4 + 8x is x2 The antiderivative of the function f(x) = %3D

A:

Q: Find the absolute maximum and minimum of f(x, y) = 4x2 + 2xy 3y2 on the unit square 0 sx s1, 0 sy…

A:

Q: Find a particular solution to y"+2y' + y =t

A:

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

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: Find the general antiderivative of f(x) 3 – 4x* + - 5VT x3 Preview 2.

A:

Q: Find an antiderivative F(x) with F′(x)=f(x)=11+24x^3+21x^6 and F(1)=0. Include a "+C" if…

A:

Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: Find the general antiderivative of f(x) = 4x 4 - 6 T + C

A:

Q: Find the particular solution of y²dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

A:

Q: Determine the particular solution. v(9x – 2v)dx – x(6x – v)dy = 0; x = 1, v = 1 O 3x° - x²y - 2y² =…

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: O For the bvp d²y - 9y = 3x, y(0) = y(1) = 0 the Green's functions G(x, §) satisfies d²G(x,£) -…

A: The greens function satisfies the homogeneous differential equation, not the non - homogeneous…

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: Consider the function f(x) = 2æ³ – 6x² + 8x – 9. An antiderivative of f(x) is F(x)= Aæ4 – Bæ³ + Cx²…

A: The given function is : f(x)=2x3-6x2+8x-9         The antiderivative of fx is the value of integral…

Q: D.Linear Homogeneous DE with Constant Coefficients: 2. (D2 – 2D – 3)y = 0 ; x = 0; y = 0; y' = -4

A:

Q: Find The Pollowrng in tograls:- Excersises 4 ( 2x + 6y x*) dy de (2 (ay + 29) dë dy + +) dy da x+4

A: As per our Guidelines we can solve maximum 3 question as per request , otherwise we solve one…

Q: dy - Find the general solution of Y +2 = 3x²y² dx A. 1/(xy) = -3(x³/2) + C B. 1/(xy) = -3(x²/2) + C…

A:

Q: The antiderivative of the function f(x) +10z is -5 - 5.0z2+c -10 +2.5z2 + c +5.0z2 +c -5 + 5.0r +c…

A: To find:∫5x2+10x dx

Q: Consider the function f(x) = 9x° + 9x' – 10a? – 4. An antiderivative of f(x) is F(x) = Ax" + Bxm +…

A: Given: fx=9x8+9x7-10x2-4

Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

A:

Q: Consider the function f(x) = 6x° – 4x? + 2x An antiderivative of f(x) is F(x) = Ax* + Bx³ + Cx² + Dx…

A:

Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

A:

Q: Find the most general antiderivative of the function. f(x) = 15x²-14x+8 O a. F(x)=6x²– 14x +C b.…

A:

Q: Consider the function f(x) = 5x-5x2 +4x 8. An antiderivative of f(x) is F(x) - Aa* + Ba + + Cx? + Dx…

A: The given function is: f(x)=5x3-5x2+4x-8

Q: - Find the solution of the separable DE 2ydy = (x + 1)dx. a. y- +x x+c c y=x'+x+C d. y=x + 3x + C b.…

A:

Q: Consider the function f(x) = 2x° + 4x" – 8x² – 8. An antiderivative of f(x) is F(x) = Ax" + Bx™ +…

A:

Q: Show that y=x² is asolution to: xy- 3xy'+4y=0, and then use reduction of order to find a second…

A: Linearly independent solutions of the differential equation

Q: Find the general antiderivative, F(x), of the function f(x) = 2x -6x² +x+ 2.

A: we will answer the first question since exact one was not specified. Please resubmit the question…

Q: Solve the follawing systen. 2 x, - 5x - cost dt dx2 b) by using the method of unde termined…

A: Given system is dx1dt=2x1-5x2-costdx2dt=x1-2x2+sint First, let us solve corresponding homogenous…

Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

A: