Describe the long run behavior of f(r) = r° – 3r° – 2r + 5 As r + - 00, f(r) → As r 0o, f(r) → ?N Check Answer -00

Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation,…

Q: 2: find fr. fy, and fz. a f(x, y. 2) = I+ xy- 22 2

A: Given f(x,y,z)=1+xy2-2z2 To find fx, fy, fz

Q: The function y,(t)=2t+e is a particular solution to y"-3y'+2y=4t-6 Select one: False O True O False

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Q: Q2) f(x,y) = 2xy x(s,t) = 3s-2t and y(s, t) = s²+4t. Find Je Je as at

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Q: d) Let y= Acos2t where A is a constant. Find the value of A such that d y --3y = 9cos2t for all…

A: Given  The equation is  y= A cos(2t) , where  A  is constant  and condition is  d2ydt2-3y=9cos(2t) .

Q: S(x) = r-6a2 +5r-8 %3D If r a at the inflection point of f(r), what is a =? SUBMIT

A: Calculate the first derivative of the function fx. f'x=3x2-12x+5

Q: 3y + 2y Solving by variation of parameter y" Wronskian W is: 3e*cosx, the value of |

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Q: Q4/ B/ If Ø = (x³y²z) and A = 2xz i - 3y²j+ 3xy²k Find 0(ФА) ay əx the point (2, -1, 3)? at

A: Given: ∅=x3y2z and A→=2xzi→-3y2j→+3xy2k→  To find: ∂∅A∂y∂xat the point 2, -1, 3 To solve the problem…

Q: re GIPTA of following is the the function P12,212) =D 31 -6f+22 Whic value of dicectional derivative…

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Q: If y is a function of x, then the equation (y – a)dx + 3ry²dy O is not + but both and with n= After…

A: This question is related to diffential equation.

Q: 5. Show that T = + y? satisfies the equation T + Tyy = T³

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Q: Find the solution. (D3 +7D2 + 19D + 13)y =0; when x =0, y=0, y' =2, y"=-12 (A y = e*cosx B y =…

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Q: Q15: Consider the D.E. (x – 1)³x²y" – 2(x – 1)xy' – 3y = 0. Is xo = 1 an ordinary point? Explain…

A: To solve the following diffrential equations

Q: 04. Show that T = satisfies the equation T + Tyy = T³. %3D

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Q: z= em and a = 2t– 2s?, y = 2s – 2t, find az at t = 1, s = 1. at

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Q: The position of a particle moving along the x-axis at time t is given by x(t) = ecos2t, 0STST. For…

A: Given: The position of particle moving along x-axis is given as, x(t)=ecos2t The objective is to…

Q: Evaluate fx and fy at the given point. f(x, y) = e¹³y sin(x), (π, 0) fx(π, 0) = (No Response) fy(π,…

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Q: xp dt of dy A particular solution X, where XeC1 -2t dt Select the correct answer.

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Q: cx + dy - f(x, y) = ; P(3, 4); u =i+ x - y

A: Given that  f(x,y)=(cx+dy)/(x-y) P(3,4) and u=(4/5,3/5) To find the directional derivative of f at p

Q: (a) Use the Intermediate Theorem to prove that Vx + Vx + 7 = 3 has a solution in the interval [0,…

A: We have to use intermediate value theorem.

Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: hup lict funcrion F(xig) = x?y -eto =0 P(e, 1) Find y" (e) = ?

A: Here to use implicit diffrentiation method for solving the problem

Q: esz+1 dz, where C:|z- 5|= 1, counterclockwise, is z - 25 The value of

A: We have to evaluate the integral ∮ e3z+1z2-25dz over the circle z-5=1. We have to find the points…

Q: Evaluate f (t) given t = 1 for %3D 12s-13 F (s) = s(s-1)(s+2)' (11+ -) 2 e e2 o 13 37 6e2 O…

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Q: Q.5 Use the one sided Greens function to solve the I.VP. y+2y'+y=8+3, y(0) =0, y'(0) =5.

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Q: g(x) is concave down at (-7,-3), concave up at (7, 10), and has an inflection point at (2, 4).

A: Given :- function is concave down at (-7,-3) concave up at(7,10) and inflection point is (2,4)…

Q: B) Find (2) for the following functions: dx u? y = u² +1 u = 3x³ -2 at p (1,2)

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Q: Find the solution. (D4 + 18D2 + 81)y = 0 A y = (c, + c,x)e²"cos3x + (c,+cx)e2'sin3x. y = (c, + c,)…

A: 16 Given differential equation is D4+18D2+81y=0 We have to find the general solution of the given…

Q: Q4: Find fa, fry fx and fy for f(x,y) = e*/y

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Q: a find theistance fron. the Point P(2,17 to the Line yzメ+22L

A: Line :- x+2-y=0  Point (2,1)

Q: (xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

A: As two questions are given , I will solve only the first one. Given : f(t)=3+e4t-te-2t+e5tcos3t+6…

Q: 3 S(x) = 6x² + x – 7 Find the coordinates of the point of inflection on and prove that it is a point…

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Q: Q#8) Find a suitable Linearization for f(x) = Cx + Dx³ (Don't find C, D)

A: Concept: The Linearization of a function f(x,y) at (a,b) is L(x,y) =…

Q: Find ∫C (ez - 1) / z  dz with C being z(t) = eit for 0 ≤ t ≤ 2π

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Q: | (3x+-x²) dx=Ax° + Bx² +C, for Suppose that %3D constants A, B, C. What is the value of C if the…

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Q: Q2: * Q2: y" + ay' + by = f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t? – 1 %3!

A: Giventhat:¯y+ay'+by=ftand yp1=et+t2-1 and yp2=e2t+t2-1To find:¯a,b and ft

Q: Find the value of n in the function w = x •rn satisfies the equation Wxx + Wyy = 0, where r2 = x² +…

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Q: Determine the r values for which the f unction y(x) is solution of the x² + 1 equation y – 2xy? = 0

A: We have to find

Q: The function y,(t) = 2t+e' is a particular solution to y" – 3y' +2y=4t-6 Select one: O True O False

A: The given statement is

Q: nd the linearization of f(x)= {Vx at c = 64. Use the linearization to approximate 64.05.

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Q: Q.1 Put the D.E (x – 1)y" + 4.xy' + Ay =0 , in self-adjoin form .

A: If the diiferential equation is a0xd2yd2x+a1xdydx+a2xy=0 then its self-adjoin form will be…

Q: sketch the odd and even extensions for -3,3]. Use the substitutions : '= ye¯* s = x Q.3 to solve the…

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Q: (a) The temperature in an auditorium is given by1=x +y =Z A mosquito located at (1, 1, 2) in the…

A: Given T = x^2 + y^2 – z We have to find the direction derivative here to get maximum temp. Gradient…

Q: SOLVE THE NHLDECC USING UNDETERMINED COEFFICIENT. (D³ + 4D² + 9D + 10)y = -24e-* when x = 0,y = 0,…

A: Topic:- solutions of differential equations

Q: h(t)= -2t^3 + 23t^2 - 59t + 24 Why do you think this model's practical domain is only valid from…

A: Polynomial function

Q: Q.5 Use the one sided Greens function to solve the I.VP. y"+2y'+y 8+3t, y(0) = 0, y'(0) = 5.

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Q: T/2, 1) S7[tan³x + tan³x]e=tan²x %3D 1/2

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Q: Find the solution. (D4 + 18D² + 81)y = 0 A y = (c, + cx)e²"cos3x + (c,+cx)e²"sin3x. B y = (c, + cz*)…

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Q: What is the annihilator for y=x e*cos 2x ? A D2+5 B D2-2D+5 © (D²-2D+5)2 (D² +5)2

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Q: Q2: y" + ay' + by f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t2 – 1

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