Find the follaing clifferential equation dy tay dx² : (05(3x) -I5x +7+eX Find a Sdlution n such that yle) =0, y l0)=!

Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

Q: So lve the di fferential equation dy + y - ecos x = 0,0 s x s0.5, y (0) = 0 by (a) Milne's me thod…

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Q: Find the general dafferential equatron (t) t 36y () - o lol00lution of the general solution y Co) =…

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Q: The solution interval of 2y +12≥3 or 3y 1 or y≤ -1} .B O (-∞, -1]U (1, ∞ ).CO {yly ≥1 or y<-1} DO

A: We have to find the solution interval of  2y + 1 ≥ 3 or 3y &lt; -3

Q: 4. Find an implicit solution using the substitution u= or y3ux dy dx x+xy %3D

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y()= 3x?y² becomes +z(-÷) =…

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: In each exercise, obtain the particular of solution. a. (y + Vx2 + y²) dx – x dy = 0; when x = V3, y…

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Q: dy ({})y+3

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: Sc ot'(3y)dy

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Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

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Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: Consider the following IVP: y"+a2y = 0; y(0) = 1, y'(0) = 0   Find the general solution

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Q: In each exercise, obtain the particular of solution. a. xy dx + 2(r? + 2y?) dy = 0; when x 0, y = 1

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Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: y" — 5y' = x − 2, when x = 0, y = 0, y' = 2

A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: Evaluate: S ndy 2y+3 (y 1)(y 1) In G) ny² + y + 1| - arct arctan 0 Inly 1| ž(y 1)* nVi y arctan( ) c…

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Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

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Q: Use the IVT to show that e−x2 = x has a solution on (0, 1).

A: Given equation is

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

A: Answer is mentioned below

Q: find following timia the exist Pim 1t y ス→。 fim (2'tyo) In (xty?) ()

A: For a function f(x) the expression limx→af(x)=b means that the function tends to value b when domain…

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: (b) Solve and by applying chain rule if z = In(x² – 2y), and x = : az u + v, y = e".

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Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

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Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: dy dx + 3x²y = 6x²

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Q: Is a solution of the diffrntish epuation 1 yy'= -X+ with y E € ]_9,GE with x € C-G,G] 2. 3)yy:…

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Q: Solve the following Bernoulli DE's. *+ x*y = x®y? a) b) y' - = y %3D

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Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: Solve the fello wing differntial equation by ieg Lapla ce trans frmation dy +2y=0, dt , where…

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Q: 2 I| ysin(xy)dydx Н.W.

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Q: 3. Find the genesral Solution: y* 5y^ +3y' -ay=

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Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

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Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.