Ex:@ Suppose thet the tallowing transformutioun Conneciãs the (x') and (xi) cordnate ار ک هأولاS sa4ス?) 2 = e えスー (x'-x²) @ Calculate the TJa cobian mutux J andj' a O Compule J

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: S Jiet'. dt Hint: use +he fundam ental theorom Find dy if dx y = of Calculus

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Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

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Q: Prove the formula.

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A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: sec( c)+y dy e sec do

A: Given differential equation is homogeneous equation

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A: The distance of a point (x, y) and the origin can be calculated as follows.

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

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…

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Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

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Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: Resolver por transformada de laplace  Y"+4y=cosx.  Y(0)=1  y'(0)=1

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Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

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Q: Let u = exsin(y), where x = -(1/2)ln(t) and y = (pi)(t). Find du/dt when x = ln(2) and y = (pi/4)

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Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: 47. Let gd(y) = tan¬1(sinh y). Then 1 cosh y = d 1 sech y dy 8d(y): 1+ sinh² y cosh y where we have…

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Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Find the efeneral Solutim Of the differential equatim: (0?-40+3)y=x+ee+x?

A: Answer and explanation is given below...

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

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Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

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Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: of the Befor to the imce beloc Evaluate the Ratiqulansoutio differential eguation land find x whe yt…

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

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Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: show that the differential eguation is exact, then solre that method using 2 2 dy- x²-x+y? |

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: If Z = Jxy +y, x= cos 0 , y= sin 0 when 0 dz By using chain rule find de

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Q: S tan ax secex dx 3

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Q: 1. xy + z2

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Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: dz Different iate implicit ly to find and if z'yz + In(ry) + sin(yz) = 10. ду

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Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

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Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: sech 2t dt Evaluate 3, coth 2t

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Q: Find the total differential. z = 6x *y5 iz

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Q: Find y't yu 4=In(sec 9x +tangx)

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Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

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Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

Q: Approximate Ay using differentials for y = x2 - 4x at x = 6 when Ax dx = 0.03.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.