Let h(x)=f(g(x)). If g(5)=−3, g′(5)=−4, f(−3)=−1, and f′(−3)=−5, find h′(5)

Q: Determine the coefficients of the equation y-ax'+bx²+cx+d so that it will have critical points at…

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Q: 5T 1 y=-2cos(Gx+っ)+1

A: Phase shift: -5π

Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: particular

A: We find particular solution.

Q: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

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…

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Q: 9-y" - 2y +2y=e; y(0) = 0, y(0) = 1

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Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

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Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: 1. Eliminate the arbitrary constants on the given equation: y = C1 + C2e¯ -2x 2 Eliminato

A: Given

Q: Q1) find the critical point of the following equation - g(x, y) = x² + y² + 2xy − 6x - 3y + 4

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Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

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Q: find the general equation of : x^3dy+xydx=x^2dy+2ydx  ;y=e when x=2

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Q: Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

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Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: Give a particular solution for y" – 2y' + y = 1+x2

A: Given that a differential equations - y" -2y' +y = ex/1+x2.   We know that integration of 1/(a2 +x2)…

Q: I Eliminate the arbitrary constants y = x²+ ax + be*

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Q: eliminate the arbitrary constant for: y=x^2+c_1 x+c_2 e^(-x)

A: Given y=x2+c1x+c2e-x                               (1) On differentiating both sides, we get…

Q: Find a particular solution for: y" - 3y' + 2y = te*

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Q: 3. Eliminate the arbitrary constants by isolation of constant y = x + C₁e* + С₂e-²x

A: In this question,  will form the differential equation by eliminating the arbitrary constants from…

Q: Apply the Gauss-Seidel method to the system

A: the Gauss-Seidel method to the system x1 - x2 = 1 and 2x1 + x2 = 5 with initial approximation [0  0]…

Q: t² - t dt 0, = (x)6 g'(4) =

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Q: Find the general solution of y" – y' – 2y = cosh 2t.

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Q: Let_y=x² +5x³-4x+1 then dy- ||

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Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: Use the IVT to show that e−x2 = x has a solution on (0, 1).

A: Given equation is

Q: Find the General and Particular solution of = 3y ; y = 3, when x = 0

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Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: ) Give a particular solution for y" – 2y' + y = 1+x² *

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Q: 5 Use implicit derivation to find y. x² +y +z =e"-

A: Given,           x2+y2+z2=exyz

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

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Q: -V4-x² c3-x²-y² xdzdydx, 0. 0, J-5+x²+y²

A: We will find out the required value.

Q: From the given equation below, compute x1X2, and X3 using LU decomposition. X1 — 3x2 + Xз 15 ЗX1 +…

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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 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: What is the DE for A(x^2)+Bx+C using elimination of arbitrary constants.

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Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

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Q: If ƒ (x, y) = ln (x² + y*) then find fy. 4y³ x4+y4 x4+y4 x4+y 4y x4.

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Q: eliminate the arbitrary constant for: y=c_1 x^2+c_2 e^2x

A: y=c1x2+c2e2x                                                           (1) On differentiating both…

Q: note that X - y +z = e2 and 4x – 3y + 2z = e2

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Q: . A woman saved GH¢ 30,000 in a bank A, whose rate was x % per annum and GH¢ 20,000 in another bank…

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Q: 1+x² »" – 2xy' + 2 y = 0 y (x)=x

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Q: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: determine the general solution of y''-y=0 given y1(x)=e-2x using reduction of orders

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Q: For the function f(x, y) = 4x³x² + 6x - 7, find the solution from x = 0 to x = 2 with an increment…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

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Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

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