dy We wish to find the solution to dæ = x°y that passes through the point (x, y) = (1,3).

Q: dy =/x y+5v xy is a Bernoulli equation dx The DE: Select one: True False

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Q: h- 0.5y" + y' + y = a*u(t) ere: u(t) = b*sin(wt), y'(0) = y(0) = 0 {a, b and w are constants} %3D

A: Given differential equation is 0.5y''+y'+y=a*ut where ut=b*sinwt, y'0=y0=0a,b,w are constantsfind…

Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: z 3e*3S,y 3z2 + sin(z)s G dx

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Q: b) Given y= ae¯* sin(x+b) where a and b are constants. Show that d²y -2x dx +5y=0 dx

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Q: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: Solve the Bernoulli equations given below dy, y dx 2x %3D

A: Given:

Q: If yo is the particular solution of dy 4x y, y(0) = 3, dx find the value of yo(2).

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Q: 16. y' + (2/t)y = (cos t)/t, y(n) 3D0, t> 0

A: The given DE is: y'+2ty=costt2

Q: xdy + (y – cos x)dx = 0, y() = 0 0, У 8. Solve the IVP:

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Q: dy 4 The equation ay = xy can be classified as FOLDE and Bernoulli's equation. dx

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Q: dy 2х+y 9. Find the general solution: %D dx x-2y а. sec x + tan y b. ху" — у' — 0 с. х? — ху + у? %3…

A: Substituting y=vx

Q: If f(0) = 0 and f'(x) E (0, 1]Vz E [0, 1] then ( red) %3D can not take values S(=)*dz

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Q: ne ordinary oliffanential e2uation 0=dx-dy homogeneous equation %3D

A: Since you have asked multiple questions, we will solve the second question for you because the first…

Q: dy + x2 4 The equation = xy can be classified as FOLDE and Bernoulli's equation. dx A True В False

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Q: dy_2y 1. Verify that x'sinx is a solution of -2-y = y cot x dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: dy =Vx y+5/xy is a Bernoulli equation dx The DE: Select one: True O False

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Q: (1+e*y+xe*y)dx + (xe* + 2)dy = 0 %3D is not Exact equation ylgn ihi

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Q: Find ôt And Ow From the equation : ôs 2. .2 x² + y? + z?; x = cos st, y = sin st, z = s?t a w = b w…

A: Please see the answer in Step 2

Q: dy d. x = y + y³cosx dx е. dx - y = 2xy²e-*

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Q: dy x2 (b) Find the general solution to the DE cos? y dx

A: As per our guidelines only one question can be solved. Solution for "b" is given below in the next…

Q: dy = 2y-2 find the solution of dx

A: dydx=2y-22-ydy=dx4 Integrating w.r.t. both sides- ∫2-ydy=∫dx4∫2-ydy=x4

Q: dy +p(x)y = Q(x)y" dx Bernoulli equation .B Exact Equation .C

A: Given that  dy/dx+p(x)y=Q(x)y^n To find the type of equation

Q: d'r =-32k, fferential equation: dt2 dr = 8i +8 j, r(0)=100k. dt %3D tial conditions: It=0

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Q: dy sin(r-y). dr Q(3) Find the general solution of %3D

A: we have to solve the given differential equation

Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

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Q: d. Bernoulli's equation y' +y = e*y+ 1. 2. xdy + ydx = xy?dx

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Q: (a) Find the particular solution of dy, 2y cOS I y(T) = 0 dx

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Q: = cos?y is dx The general solution of the DE

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Q: d Y+6-40 y=0 dy Determine the general solution of dx? dx

A: Given d2ydx2+6dydx-4oy=0

Q: arcsin = ab' a? - Va? - y?; Find y!. Oy = 2abr(x+b) Va-y 1-y 2ab r Va- 1-y 2ab r/a-y H. 1-2ab z a- «…

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Q: d'y dx di y (x,0)=sin Tx ,t=0,0 ≤ x ≤l 8 dy (x,0) Solve the equation and with y (0,1)=y (1,r) = 0…

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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: Obtain the general solution of the equation d'y dy + 3 + 2y = 10 cos 2x %3D dr dr Find the…

A: We have to find roots of characteristic equation first.

Q: dy 5. Using Euler's method, find y(0.02), y(0.04) and y(0.06) given- dx correct to 4 dp. y-x x+y…

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Q: 3. dy + y dx - 2xу?е* dx %3D

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Q: Find the particular solution of (xcos? - y) dx + xdy = 0 ; where y and x = 1 - у %3D = - 4

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Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

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Q: dx Reduce the given DE into Bernoulli's equation: = 3x³y? y dy +

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Q: Obtain a solution to this linear equation. dx − (1 + 2x tan y) dy = 0

A: Given that: dx − (1 + 2x tan y) dy = 0

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: z = x+ y dy _ x+ y+2 1. Using substitution solve the equation which satisfies the condition y(1) =1.…

A: Use the given substitution to convert the homogeneous differential equation into separable form then…

Q: dy +3 dy -4 y=e* . dx dy Problem 8/ Knowing that at x=0, y32 and dx find the specific solution of…

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Q: dy =f(x.y). y(x)-yo is dx By Picard's method, the third approximate solution of a. Y3 Yo+ b. None of…

A: We need to find the third approximate solution of dy/dx=f(x,y) , y(x0)=y0 by Picard's method.

Q: A) The position of a particle P(x, y) at time t is given by: x= (2t + 3)i , y =+t.Find the distance…

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

Q: z = x+ y dy_ x + y +2 1. Using substitution change the dx x+ y+7 to a separable equation, Hence…

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Q: d²y then dx² cos x 2 dy Show that if y -+y = 0 x dx %3D

A: Given: y=cosxx To show: d2ydx2+2xdydx+y=0 Differentiate y with respect to x using the quotient rule…

Q: dy 2x+y 9. Find the general solution: 2 dx x-2y a. secx + tan y = c b. xy" – y' = 0 с. х — ху +у?…

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Q: y" + y = 8(t – 37) cos(t), y(0) = 0, y'(0) =1. %3D %3D

A: Consider the provided question,