TIon 3 By using completing the square, dx can be rewritten as Vx²-4x -7 1 dx V(r-2):-3 1 dx OB. J V (r-2)2-11 1 dx V(r-2)2+3 Oc. None

Q: If 3y-5x = 7, then at (-1,2) is dx %3D

A: This problem can be solved by differentiating the given implicit equation w. r. t x and then finding…

Q: (a) (3-x- y)dy=(2x – 4y+6)dx.

A: According to the guidelines I can solve 1st problem only. For the remaining problems you have to…

Q: 6. |x²e-2*dx

A: Solved below

Q: (a) By using the substitution, u = 1 + x*, or otherwise, find x3 -dx 1+ x4

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Q: If 4x²-2y²=9, then find dy/dx.

A: Using defination of differentiate

Q: a) 2 7e"- dy

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

Q: 3. 9x -dx (x² +7)

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Q: a. Jx-2 + 6x² dx Jr b. Setanx sec²x dx tana c. S 2x+ 6 dx x2-3x,

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: 2x - 4x – 8 -.dx Find -3)(x* +4)

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Q: Find the general solution of = 8e-4x %3D dx

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Q: x² – 16 - dx = Mx + 2)3

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Q: of Find (1.-7) if f(x.y) = 2x2 + 4xy - 5y? + 4x - 9y - 9. dx of (1, -7)-O (Simplify your answer.)

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Q: 13) Find / VI- 2x dx by the method of substitution.

A: Substitute   1-2x = t

Q: Question d²y Find if-x2 + 3y² = 4. dx2 Provide your answer below:

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Q: 25+1 c) r³-3x²-10x dx

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Q: Evaluate by any applicable method. 1/2 5-x So dx 4x2+1

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Q: ,3 dx 3 Vx²-16

A: Given integral I=∫x3x2-163 dx

Q: Find if-10x – 6y = -6. dx2 Provide your answer below: %3D dx

A: We Have to find second order derivative

Q: cosh 3x-1 S - dx 2

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Q: 3. 2(2x2 + у?)dx — хуdy %3D0. |

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Q: 3/2 (-2x + 4) dx J1/2 | 16.

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: о dy-bdy +ay 1 dx2 - бе 3х +те-го года

A: The objective is to solve the given differential equation. Since the given equation is non…

Q: [D3 – 6D2 + 11D − 6)y = cosx sinx

A: The objective is to solve the above differential equation.

Q: By using completing the square dx can be written as V4 + 2x + x2 dx 3 +(x+2)2 dx V4+(x+2)² dx 3 +…

A: Given, ∫x4+2x+x2dx  We have to write it again using completing the square.

Q: d²y — 6+ 13у %3D0 dx2 dx

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Q: 42. (a) By completing the square, show that 1/2 dx T x² – x + 1 3/3

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Q: Evaluate the integrals

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Q: Show that (xcos(2x)dx=. A-2 8

A: LetI=∫0π4xcos2xdxPut 2x=udifferentiate on both side2dx=dudx=du2As x→0 then u→0As x→π4 then…

Q: dy Solve dx = 6 if y(1) = -2. О у/х) %3D 6х —- 2 О У/х) 3D 6х - 8 О у/х) %3D 6х + 8 О ух) %3D 6х + 2

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Q: (x² + 4)³/2 -dx

A: Given integral is: I=∫x2+432xdx Integrating it: Put:u=x2+4dudx=xx2+4dx=x2+4xdu…

Q: dy +2x². dx3 dy dx2 + x- dx - y = 0

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Q: ( 2x-sy+12) dx +(7x-4y+15)dy = o 2,

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Q: Find the value of b so that (2x – 1)dx = 10 - 1 3 O 2

A: We have to find out b

Q: In the last part of step 1 for ds/dx, where does the 1 under the square root go? Why does it just…

A: Let's solve.

Q: Solve the egjuation ditferential (2x-3y+5)dx+(3x-2y+2)dy=0

A: Given the differential equation is                     (2x -3y +5)dx + (3x -2y +2)dy = 0

Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: is Substitute for +4 X = 2tano and dx= 2 Secodo %3D

A: Given integral is ∫x3x2+4dx Substitute for x=2tanθdx=2sec2θdθ

Q: A) Evaluate 1 dx. I vit 6x – x² -

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: ¹₁¹+x² x + 2y dy dx -12x²

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Q: Let y = 4**-2x+3. Find d²y - dx2°

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Q: +j =6- d 5x+(/x + %3D dx x² 2.

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Q: 7. ex-4e-3 dx x- A 2 x + + С 2 + С et В х+2 е х + О D х - 2 е * + С

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Q: If x3 + y3 = 16, find the value of d2y/dx2 at the point (2, 2).

A: Given:

Q: -3 ³₁₂₁(4x²y - z³) dz dy dx

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Q: dy *+ 2xy = 0 dx 6.26. у - 3x4у %3D0

A: The general form of a linear homogenous differential equation is given by dydx+Py=Q. The solution of…

Q: By using completing the square dx can be written as /4 + 2x + x2 dx 4+(x+2)² dx V3 + (x+2)² dx V3+…

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Q: 3 Evaluate: 2₁ (4x²yz - 2 ) dz dy dx 4

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Q: Find Jog %3D 1-cosx dz n=770

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Q: dy - 2x + 5 y --(1) dx 2x+ y

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Q: 3 2 - VX dx x² – 4 1 2]

A: ∫12xx2-43dxLet u=x2-4.=∫-3012u3du=12·∫-301u3du=1232u23-30=12--123· 323·32=-3-123· 3234

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.