If x= 2u3 – 3u² and y=u³ – 3u, then dy is dx u+1 (A 2u u+1 B и — 1 2u и — 1 D

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: Sy+1-2 dy, can be evaluated conveniently if we let y+1-2=t and dy = 4r(r +2)dt.

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Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: Reduce the DE with linear coefficients (6x + y-9) dx + (x – 2y+5) dy=0 to a homogeneous DE. A ( 6u…

A: Given ODE, (6x + y - 6)dx + (x - 2y + 5)dy = 0 To reduce above ODE to homogeneous ODE.

Q: If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2

A: Given u=x2y+y2z+z2x. Find dudx as follows.…

Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: Let w = 4e" dx /A dy + aeª dx ^ dz and n = 7e*Y dx + 8e² dy + eY dz, where a E R. Find the value of…

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Q: 3. Given: y = f (u) and u = g(x), find dy/dx: 2u d) y = u2+1)' u = 10x2 + x +1 e) y = u+ cos-2 u, u…

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Q: • If u = x+ 1 t=yu y t then, %3D 1. dy =D0 dx dy dx dy = 1 2. 3.

A: The given functions are u=x+1, t=u  and y=t2. Convert the function y in terms of x as follows.…

Q: H.W: Solve-Using D-operator dy dx dt ™ dt + 3y – 5x – e-t = 0 %3D dx dy 2 ++x + y – 3 = 0 dt dt

A: Answer is mentioned below

Q: • If u = x+1 t= yu y= -t² then, %3D dx dy 2. = X dx dy 3. dx %3D dy 4. :-1 dx I||| 1.

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Q: z=9x + 4y + 1 dy = (9x+4y+ 1) 2 reduces to dx Using the substitution the DE -- dz=9dx+ 4dy

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Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

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Q: 2 1. The cissoids y : %D а —х

A: Given the equation  of cissoids y2=x3a-x As per our guideline we are supposed to answer only the…

Q: Find the particular solution to DE:  ( xy^2 - x ) dx - ( 2x^2y - 3y ) dy = 0 ; y ( 1 ) = 2

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Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: 3. Given: y = f (u) and u = g(x), find dy/dx: %3D 2u d) у 3 u = 10x² + x + 1 (u²+1)' e) y = u+ cos'…

A: We have to solve given problem:

Q: Find dy/dx if y = x^3/2 by using the Chain Rule with y as a composition ofa. y = u3 and u =…

A: a) y=u3 and u=x     dydu=3u2anddudx=ddxx       =12x-12 So, dydx=dydu×dudx      =3u2×12x…

Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: y y" – (y')? = 0 where * = y'. If consider dæ u = y', then the D.E. is reduced to (A) Y dy du u? (B)…

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Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: _1. y +1-2 dy, can be evaluated conveniently if we let y+1-2=t and dy = 4r(r +2)dt. %3!

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Q: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

Q: D. Identify the linearity of the following equations. y°dx + xdy = sin y dy 16. dzy +x- dt2 d?x 17.…

A: Given that:                                 NOTE: As per our answering guidelines, we can only…

Q: 3. Solve the DE dy a. = x + 2x dx 3 dy b. dx dy C. = 4 cos 6x - dx 4 dy d. dx %3D x2-1 dy e. dx %3D…

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Q: dy B] If y = e" In(u) and u = V1-x2, Find dx

A: To find

Q: 3. Given: y = f (u) and u = g(x), find dy/dx: a) у%3D сos u, и%3D—х/3 b) y = tan u, u = 10x – 5 - с)…

A: Our aim is to find the derivative of the above expressions.

Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

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Q: The differential operator (D – 8)(D+2)y= O (D² – 6D + 16) y O d'y 16y | dæ² dx O (D² + 6D – 16) y…

A: Topic = Differential equation

Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

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Q: H.W: Solve-Using D-operator dy dx + dt + 3y – 5x – e-t = 0 %3D dt dx dy + x + y - 3 = 0 dt dt 2.

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Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: If the substitution m = 2x - y was applied to the DE: (2x – y+1) dy + e2-dx = 0, the resulting DE…

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Q: If y=7x²y+z³ +yz² A = y³ z² e^5x a_x + 4x4 zcosy a_y+ 2x4 CosySinz a_z. Find the following at point…

A: Given, ψ=7x2y+z3+yz2A=y3z2e5x ax+4x4z cosy ay+2x4cosy sinz az           Note: The expert is supposed…

Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: Solve the DE shown below: (1 Point) (x + y - 3)dx + (5x + 5y – 2)dy = 0 O 4x – 20y - 13 In (4x + 4y…

A: Homogeneous differential equation

Q: Solve the Euler equation d²y dx dy -5y = 0 dx 31 d', 3x2 given that y(1) =1 and y'(1) = 2. intai

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Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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Q: a. Find of the following. dx 6. x = Vy3 + 3y 3y+2y2 7. x = 2-y2 8. x = 2u3 – 3u? and y = u³ – 3u и…

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Q: 20x -4Dx Dy t40y )u= cos(2X+y)+xy Ans. U= i(y-2x) +x2 (9-2x) + Coslzx+y) +

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Q: (ii) (D² + D')u = cos px cos qy u = cos px cos gy (iii) (D²- DD'- 2D)u = (v - 1)e*

A: In the given question we have to find the solution of second and third part of the given question,…

Q: Find dy/dx and d62y/dx62 at the given point without eliminating the parameter. x=1/2t^2+9…

A: Given parametric equations are: x = 1/2t2 + 9 y = 1/3t3 + 4t Differentiating x with respect to t we…

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: 11. Ay≈ f'(x) dx III. y2y₁ f'(x) dx - Oll O III O None of the choices OI

A: Using definition of derivative