et F = t+3 2i-fj+3t°k and G = e'i – 3f j+ e²* & %3D

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: 37. - dy y. dt

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Q: Use the Euler method with dx = 0.5 to estimate y(5) if y' = y2/√x and y(1) = -1.  What is the exact…

A: In the given question, it is asked to solve a differential equation using Euler’s method.

Q: EVaLuate W= X -*-cos't ,y=cost sint

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Q: Determine the integrating factor of the Bernoulli's equation given pelow: dy -y cot2x = y' csc2x dx…

A: ................(1) substitute take derivative .................put it back in equation 1

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

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Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

A: Given

Q: dx S COsxtanx

A: Here we will solve the given integration,

Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: Use the Euler method with dx = 1/3 to estimate y(2) if y' = y - e2xand y(0) =1.  What is the exact…

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Q: dy tan tan x = 0 dx coscos x +

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Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: solve the IVP x(1-siny)dy=(cosx-cosy-y)dx y(π/2) =0

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Q: find dy/dt. y = sin (cos (2t - 5))

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Q: In(5x +3) dy at x = 0. dx (a) If y = then find et

A: Given; y = ln(5x+3)/e5x

Q: The degree and order of the differential (出) 1 8 dy equation 1+ is 3 dy dx dx

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Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: The order and degree of the differential d³y V dy equation: 7+ is dr3 dx 3,2 7, 3, 3, 1 3,7 Question…

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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Q: 1) ſ y³ sin(2y) dy

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining questions…

Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: Ssin (2x)cos(2r)dx

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Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

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Q: Find the integrating factor: cos⁡ x dy+[(y sin⁡x )-1]dx=0

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Q: The integrating factor of the equation sec? y + xtany= x° is: dy de In|sina| O None of these…

A: We have to find I.F

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: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

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Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: dx-(it 2x tany) dy-0

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: The degree and order of the differential 1 dy equation 1+ is 3 dx wy dx

A: Solution

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

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Q: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: Can you help me step by step?

A: Given information:

Q: Find an integrating factor depending only on x that will make 2ye 5x* 3 sin y + 5xex + dx + (x cos y…

A: Given:            Let the differential equation is in form 3siny+5ye5x+2ye5xxdx+xcosy+e5xdy=0…

Q: 1) S 2 sec y (tany – sec y) dy

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

Q: dx o ex+x е. f. S sin(vE) dt S dx 2x cos(vE) dt COS g. dx 'x

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Q: Solve the differential equatic y' = (x + y + 2)², Chart Area y(0) = 2 by setting u = x + y + 2.

A: y'=x+y+22let u=x+y+2     u'=1+y'     y'=u'-1

Q: dy - 1 = siny dx

A: Given : dydx-1=siny To Find : solution of Given DE

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.