Consider the following. 9x4 - 8x - 1 y 4 - x2 Find the value of y when x = 1. y(1) = 0 dy Find dx -18 + 144r3 – &x² – 2r – 32 -18r5 (-x² + 4)² - &x2 – 2x – 32 dy dx

Q: 2-x2 Evaluate Jenyz dy dx x²+y? 2 Select one: a. Non of them b. 1 /2 C.

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Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Q4)/ Solve the Following: d²y dy 4x - 6y = x³ + 1 dx² dx

A: See the attachment

Q: 8. (D2 – 10D + 34)y = -cos3x

A: Answer and explanation is given below

Q: dy If 3x -1 and if y= - 1 when X=1, then y= dx A x³ - x-1 x³ +1 © x³ - x+1 D -x3 + x-1

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Q: Evaluate the following problems by obtaining the general solution. Show complete solution.…

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Q: for all of dx 1- y = xvInx 2- y = 3 x(x-2) x²+1

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Q: Try this: Solve the following DE. 1. (x-3y + 2)dx + 3(x+3y-4)dy = 0 2. (2x+3y-5)dx + (3x-y-2)dy = 0…

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Q: 3. (10 – 6y +e 3) dx -3x 2dy = 0 -

A: According to our guideline, we can solve only first question of multiple question. If you want…

Q: 1. SE-0) dx =- SE-D) dx 4 In|x| +C А. 4x %3D 8. В. 4* _2. dx = 6Vx + C %3D С. 4 3. s(3V+) dx = (x…

A: Disclaimer: Since you have asked multiple questions, we will solve the first three questions for…

Q: dx 2*+1-5x+1 (a) (b) [ cosh*x dx, (©) Jarcsin x)²1-x² dx, (c) 10* [In(v + 1)]² v +1 (e) T20 -02 (d)

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Q: Differentiate. y =xe -9x + 4 e Choose the correct answer below. OA. O A. dy - + x6- - 9x - 4 e "X +…

A: The given function is y=xe-9x+4e-x+x6.

Q: d²y Find particular solution for + 4 + 4y = 3xe dx dx

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Q: E 34 ,8-23y² dz dx dy 3-3X p3-3X-y SSS(x+y+2)dy dx dz

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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

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Q: 12. (2xy³ + 1) dx + (3x²y²-y¹) dy = 0

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Q: а. (4x3 — 6ху^)dx + (4y- 6ху)dy %3D 0 b. 1 -(xdy- ydx)=0 x²+y? с. 1 (v²dx+x²dy)=0 (x2-у?) d. (x+y)dx…

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Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

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Q: 2xy - 10y -x + 5 y - 6 xy + 5y + 2x + 10 -dx +- 0 %3D 2.x + 3

A: Separable Differential Equations: A separable differential equation is an equation that can be…

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

A: Let's evaluate given double integral.

Q: 8. (x² + 2xy 4y²) dx - (x² - 8xy - 4y²) dy = 0. ANS. x² + 4y² = c(x +

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Q: x+ If y = dy will be dx then 2х- 3 (2x – 3) (1 – ) - (2x + 3) A. (2x 3)2 (2x – 3) (1 +) - 2(x+) B.…

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Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

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Q: 2X 2x -ë dy+2lyê¯-x) dx =e

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Q: 3. (x - 1)dy - x?ydu = 0 4. (x2 - y2)dx + xydy = 0 5. (x2 - y)dx - (xdy – ydy) = 0

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 3x3 d'y If y = + find dy and dx (a) 3 2 dx2 (b) If f(0) = 4 cos 30, find f'(0) and f"(0) and…

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Q: Find the particular solution: (y4 – 2xy) dx + 3.x² dy = 0; when x = 2, y = 1 %3D

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Q: 3y(x? - 1)dx + (x? - 8y - 3x)dy = 0 when x = 0 and y = 1 A xy (y - 3) = 4(1 - x²) B y (x² - 4) =…

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Q: 2x+2 dx then B- %3D x2+10x+24 x+6 x+4 Oa-6 Ob.5 O10 e d.-3

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Q: If $S² A 2x²+x-2 (x+1)(x²+1) (В NIG NI- S None -dx= B(2x) +C1 14.0+. dx, then the value of B is…

A: We can answer the question for the value B as below.

Q: Find :a. b. 20 fő -1 20 dy (1+y) ² (20-6x) e 20x - 3x² dx

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Q: y(x - 6y)dx - x(2x - 9y)dy = 0; when x=1, y=1 a. y?(2y-3x) = 3x2 O b. y?(2y+3x) = x² c. y2(3y-x) =…

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Q: 1. Find the dy of the followings: dx (iii) y = (4x² – 20)(6x + 5) (iv) y = (4x² – 20x + 50)6

A: For given (3) and (4) , we have to differentiate it with respect to x

Q: Find (D2Y/DX2) for y=e-4x^2

A: We have to find second derivatives of the function: y=e-4x2 We will use following formulae:…

Q: x³-2y2 dy f) dx Hint: You know two methods that will work! 4xy

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

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Q: (x² - 2xy+3y-7)dx + (3x − x² + y³)dy = 0 (2y + 1)dx + (x + 2) dy = 0. y' + 5y = e-3x

A: 1) x2-2xy+3y-7dx+3x-x2+y3dy=0 solve the differential equation differential equation is of the form…

Q: 4. Find the general solution for the DE below: a) = x b)= 3r²-1 dx 2s

A: Seperate the Variables before applying the integral.

Q: B. 1. 2. 3. Find dy for the following equati dx X²+y²2-2x+3y=0 1 = 4 x² + y² x³+y³+4xy=5

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Q: Question 2 Find for dx (a) y=(5x³-3)(x²+4x-1) (b) y=√x(2x²-3) dy (a)=25x¹+80x³-15x² - 6x - 12 A dy…

A: Solution

Q: 4. (x² + y²)dx - 2xydy = 0 [Ans. x² - y² = cx]

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Q: (d) S 2e-2# dx 4x (e) J1dr -dx (f) S(2ax + b)(ax² + bx)"dx

A: Use the formulas below to evaluate the integrals. ∫eaxdx=eaxa+C∫xndx=xn+1n+1+C∫dxx=lnx+C

Q: x(y-3). * - xly-3) dy = x(y-3)dx nly-31= C y-3 e [y-ce 3 2. Pesticide was given to a colony of 8000…

A: we have been given an equation y'=x(y-3) which can be written as  dydx=x(y-3) here, we will use…

Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: Determine the general solution for the following: 1. ( 6x2 - y +3 ) dx + (3y² -x - 2) dy =0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 4. (D³ + 1)y = xe2x 5. (y" – y) = e-× cos(3x) 6. (D² + 1)y = - 7. (D5 – 5D3)y = 24 \マ 3

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Q: (9xy-2y2) dx - (6x²- xy) dy =0

A: 9xy-2y2dx-6x2-xydy=0dydx=6x2-xy9xy-2y2dydx=x6x-yy9x-2y

Q: 7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

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Q: d²y dy -2 +4y dx 2e 2x dx2 x3 an is given hy:

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Q: 4. y(8x – 9y)dx + 2x(x – 3y)dy = 0 a. 2x*y – 3xy? = C b. 2x*y – 3x²y² = C c.2x*y3 – 3xy? = C d.None…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.