f(x) = e−x,    n = 5

Q: dy y² tion + dx x² है || Y 8

A:

Q: d²y dy – 4 + 4y = e2t.t dt2 dt

A: our objective is to solve the differential equation

Q: Find the general solution of y' = y secx

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Q: y" + 2y' +y = e-*

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find d2y/dx2 implicitly in terms of x and y. xy − 1 = 2x + y2

A: xy − 1 = 2x + y2 We need to find  d2y/dx2 implicitly in terms of x and y

Q: y′′ + 2y′ − 8y = 2e-2x − e−x , y(0) = 1, y′ (0) = 0.

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Q: x dv (2.v) - dx (V²1) dv (1+r) dx X 2 \-2 V-V²

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Q: xsin-1x > [4) S*s dx [4] S Y1-x2

A: Here is the solution

Q: 4.Jy2-プdy

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Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: (d) Evaluate [(2xr² – 3x)dxusing formula develop in part (c)

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

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Q: -t,x-1 dt

A: Please see the explanation below

Q: Q3. Solve dy (x+3) dx S 3x, 0 3.

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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: 16- y? V16 - x2 x dx dy 2.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

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Q: z· 3°dz

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Q: Find d2y/dx2 implicitly in terms of x and y.

A: To findd2ydx2

Q: Find (a) E (Y/X= 2)

A: Answer: Using the given joint probability function for the random variables X and Y

Q: V16-x² .4 Evaluate: [4 16-x² J/x²+y² dz dy dx

A: We will evaluate the following Integral.

Q: Evaluate VA-x2 4-x2-y2 (x² + y²) dz dy dx. -V4-x2 0.

A:

Q: -x-3 F(x) = S (5t + 2) dt

A: According to question given thatF(x)=∫x3x-35t+2 dt

Q: Find d2y/dx2 implicitly in terms of x and y.    x2 + y2 = 4

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Q: What is the solution for y(t)?

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Q: Q2/ solve; A: dy - = e* * y3 dx x+1

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

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Q: y"-2y'+y = e* Inx

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Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: t² - t dt 0, = (x)6 g'(4) =

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Q: y"+ 2y' +y =e* x-

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Q: Find d2y/dx2 implicitly in terms of x and y. x2y − 3x = 8   d2y/dx2 =

A: Consider the given function, x2y-3x=8 use implicit differentiation method and differentiate with…

Q: e-X f(x, у) %3D x2 + y2

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Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

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Q: 1. y" - y' - 2y = e* %D

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Q: SSS(x² + y²) dV where E lies between x² + y² +z² = 4 and x² + y² + z² = 9

A: E

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

A: Given,           x2+y2+z2=exyz

Q: ſx = s² – t² . z = 2x – 5y, ly =s•t³ · t3

A: We find complex function

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: y, = x2 + 2x + 2 Y2 = 2x + 18 dx 25- 20 15 y 10- 5- 6.

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Q: -2 S.f(x)dx -4 a. b.5°2f1x) dx C.5f(x) dx

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Q: calculate d2y/dx2 when y=e-(x-3)-x

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Q: Solve (x² y³ + xy² + y) dx + (x³ y² – x² y + x)dy = 0.

A: Given differential equation is  x2y3+xy2+ydx+x3y2-x2y+xdy=0

Q: 2x- x2 4Vx +y dy dx JJ

A: Given: ∫02∫02x-x2 4x2+y2 dy dx The function is z=4x2+y2. To Evaluate: The iterated integral by…

Q: а a²-x² ху(х + у)dydx 0. x,

A: Integration of function expression with respect to variable x or y gives the area under function…

Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

A: