te ,t<- 3 b) Let y(t)= find L(y(t)) + sint cost 3

Q: , X= sin ztS d= In Find dw 2- Cost

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Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: cosh x dy + (sinh x)y = e-* dx

A:

Q: Q2/Find dx of y = sin(e') + xtan-1x. %3D

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Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

A:

Q: a) Solve etan y dx + (1+ e*) sec'y dy = 0. sin(3z + z?) b) Find y for y = (6 – z*)3

A: The given differential equations is  and the other equation is y=sin(3z+z2)6-z43 The differential…

Q: Finding a General Solution Using Separation of Variables. dy/dx= (x-1)/y3

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Q: e*dx cln 1 Calculate Jin 0.5 V1-ezx" (b)

A: We will solve this integral via substitution:

Q: Q3 using Euler method, find an approximate value of y corresponding to xe [0 - 0.7], dy Given = x(x…

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Q: 9. Sinte)e x(t² + 1)dt = x ,(t² + 1)dt S' 2* dx < S, xdx 10. dx = dx + dx 11.

A: 9.∫ln(e)0ln(e)ex(t2+1)dt=x∫0e(t2+1)dt10.∫012xdx≤∫01x dx11.∫131xdx=∫151xdx+∫531xdx

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: ) L -dx (x² + 1)²(x² + 2x + 2)` sen? t dt, for 0 <b< a. a+b cost

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Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

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Q: y3 r³ – 4x – 1 = 0 3 Find dy/dx and explain why dy/dx is always positive. Where on the interval [0,…

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Q: tan x d. y = sec? t dt 3 е. y = dx 1— х2. its

A: We have to find dy/dx for the given function

Q: d etermine whether or not diffential eq is exact (1/x^2 - 1/y^2)dx + (2x+1 / y^3)dy=0 if exact solve

A: given differential equation is  (1x2-1y2)dx+(2x+1y3)dy=0

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: sinh x d Find dx 1 dt t2 + 1

A: We will apply Leibnitz theorem to solve it

Q: dy 3 sinh y - 5 cosh y

A: Given, I=∫dy3sinh y-5cosh y

Q: dx at x = dt dy Find - 5 if y = x² - 3 and = 4. dt

A: A detailed solution is given below

Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: Sin²y dy V1 -x, given that y(-3) = 0. dx 2) Snow that the general solution for (x2 +x-6)dy = 4y dx…

A: Given that  The following differential equations

Q: g(x, y) = sin (T ¤y) + log3 (x – 3y) -

A: The given function is                          gx,y=sinπxy+log3x-3y…

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

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Q: Using dx/dy solve sin(x+y)-cos(x+y)=1

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Q: order differential coefficients as serie (b) y) when y = (7) sin 50. 50

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Q: d) y = 5 ln 3 ; x=2 cost sin t e) y=r° cos (2e') ; x= 3-1

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Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

A:

Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: 1. Solve for y, using the method of successive approximation. dy dx = x + y; y(1) = 1

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Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Advanced Math dy/dx=sin(x)+1 using euler method h=0.01 y(0)=1 y(1)=?

A:

Q: 31. f(x, y) = e cos y a. (0, 0), b. (0, п/2) %3D at

A: We know that linearization of f(x,y) at (a,b) is

Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: A. Integration by parts i) (3t +t²) sin(2t) dt

A: since u have asked multiple question in a single request so we will be answering only first question

Q: dy/dx=(x+siny)/(2y-xcosy) is an exact equation

A: Given that dydx=x+sinyy-xcosy we need to check that it an exact equation

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: Q3\ using Euler method, find an approximate value of y corresponding to X€ [0 -0.7], Given = x(x +…

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Q: E valuate dt + seck tan x dX

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Q: Hw #4 ( 2 xy +y -tany) dx+(x²-x tany tSeiy )dy =o ??

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…