1 f(x)=, 2х -3 11. Given and g(x) = Vx+2. Find (fog)(x) and its domain.

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: m (x) = V - 6x 1. f (x) VI +2-3 1 t(z) V9 - 1 9-r

A: we have to find the domain for the following function

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: (² + 1)³yy'(t) = 1(y² + 4)

A: Given:- (t2 +1)3y y'(t) =t(y2 +4)  To find:- General solution of given differential equation

Q: dz and dy dz 3. If x? – 3yz2 + xyz – 2 = 0, find -

A: In this question we have to find the dzdx and dzdy.

Q: By using variation of parameters answer the following for the DE: y''-y'-2y=4x^2  g) What is u2y2…

A: We have to find u2y2 using variation of parameter.

Q: 2. Using the variation of parameters, find the particular solution of (D² + 1)y = sec x

A: By the method of Variation of perameters

Q: Find the general solution of (T^2 + 4)y' + 2ty = t^2 (t^2 + 4) with the variation of parameters…

A: In this question, we find the general solution of (t2+4)y'+2ty=t2(t2+4) with the variation of…

Q: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

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

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Q: What is the value of the arbitrary constant C if the given DE is y' = 2(2x – y) which passes through…

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Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: (3x)i + (3y)j + (3z)k F = x3 + y3 + z3

A:

Q: [Q4] Applying the method of variation of parameters, solve x'y" - 2xy'+2 y = x' sin x

A: The solution is given as

Q: (b) Solve N +e*f + (1+x*)y = 0, %3D near x = 0, if y(0) = 1; y/(0) = 0. %3D

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Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: Se-2t if 0 3,

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Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: (b) Solve y" + e*yf + (1 + x²)y = 0, %3D x = 0, if y(0) = 1; y'(0) = 0. %3D

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Q: f(x,y) = (x³ − x)(x² − 1). find fxy(x, ×

A: We have given that ,  fx , y = x3 - x y2 - 1 We need to find , Partial derivative fxy . We know that…

Q: t² - t dt 0, = (x)6 g'(4) =

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Q: Find the general solution of the following using the method provided: 3. Variation of Parameters y"…

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Q: Find d²y/dx² for the following equations: e) xy + y² = 1 f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

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Q: 2 The Range (Ry) of y = v9 – x² -

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Q: Q3: if f(x)= xy+2x-5y =2 then dy/dx3D a- b- C-

A: We know that dy/dx mean difernciate f(x) with x. From this we will get our answer.

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: A. y" – 2y + 1 = (x + 1)e²x

A:

Q: + 12du = 0, t> 0 with u(x, 0) = f(x), 0 < x < 1. Determine the characteristics and sketch them.…

A: Given: The given partial differential equation 3∂u∂t+t2∂u∂x=0 with  u(x,0)=f(x),0&lt;x&lt;1.

Q: By using variation of parameters answer the following for the DE: y''-y'-2y=4x^2  d) What is W2?[No…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: [6f(x) – g(x)]dx = i if f(x)dx 5 and g(x)dx 10

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Q: E. y = xArctanx - In V1+x

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Q: 8 If f(x) dx = 37 and g(x) dx = 12, find %3D [2f(x) + 4g(x)] dx.

A: Given ∫08f(x)dx=37 and ∫08g(x)dx=12We have to find ∫08(2f(x)+4g(x))dx

Q: An insect is in a toxic environment. The level of toxicity is given by I(x,y)= 2x* – 4y If the…

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Q: H.w Solve y'+y'-zy= -2 f yoj=Zfylcojal

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Q: = 0 for F = yz²î +xyj + yzk

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Q: Find d²y/dx2 for the followi f) x2/3 + y2/3 = 1 %3D ³ g) x + y = 16

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Q: f(x) = { Sx + 2 1-x+3 x>-2 Dano

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: Find dy for the given values of x and Δx. y = 6x3 - 7x ; x = -3 and Δx = 0.3 .

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Q: Solve for fxx, fxy, fyx and fyy given f(x, y) = 2 ln(x − y).

A: The given function is:fx,y=2 lnx-y.We need find fxx, fxy, fyx and fyy

Q: Apply Variation of Parameters to find the general solution. e* у"- 2у'+ у 3 1+x?

A: Given y''-2y'+y=ex1+x2

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=…

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