e-(2²+x³) dy dæ x=-0 Jy=0

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

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Q: S when メ=2 Y =x*+b $ Find dy when X=. dt dy

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Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

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Q: dz/dy for z = e^xy

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Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: find dy/dx

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Q: Find dy/dæ in terms of t if x =t – t°, y = 2+ 4t dy/dx =

A: The differentiation of parametric form of functions can be done by using the formula,

Q: . (solve exact de) (2ysinxcosx - y + 2y?e*v* )dx = (x - sin?x - 4xye*)dy

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

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Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: dy at the given points. dx Find 5. x + 4xy + 2 y² + 3 = 0 .2 at (2,–1).

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Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: c.) S (4t²-t²+16t)dt/(t²+4) d.) S V1-cos*o de

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Q: y - cx'y' +e + sin(xy) – (ny + y@) = 0 у%3?

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Q: dy dt2 dt d'y 8x = 0 - dt?

A: Given that, d2xdt2+dydt=0d2ydt2-8x=0 Now take the derivative for the first equation with respect to…

Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

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Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

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Q: dx 2. Find the value of at y=1 if x=z³+4z and z= (y² + 2y)²/³. dy

A: We have to use chain rule while differentiating.

Q: dy +y de : 2 et dx Arowar 1- ye" (c -x*) 1= yet (c -x*) %3D

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Q: 8. (/E= + y² - y) dt + (y/E² – y? - t) dy = 0; when t = 3, y = 4 %3D

A: Solution is  ty=3(t2+y2)3/2 -363

Q: dy dæ 2 and dt at x = 3 if y = 3x? 4. Find dt

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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: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: z=9x + 4y + 1 dy = (9x+4y+ 1) 2 reduces to dx Using the substitution the DE -- dz=9dx+ 4dy

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Q: Find dy/dx in terms of t if x = te', y = 4t + 4e* dy/dx =

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Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

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: dx Let y = 0.75a? + 4.25 and dt 0.6. dy Find when x = 3. dt

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Q: d'y dy 4+y =r²-21 +3 dt? dt

A: We will calculate CF and PI separately then we will add them.

Q: What is the solution of the DE e dx – x² dy = 0? A. y = (c - B. y= In (c - C. y = In (c - x) D. y =…

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

Q: ind the differential dy. y = V15x² y =

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Q: x²y(cos(Tz) +2) dæ dy dz

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Q: dy - f *P, = 7 dt y(0) = 4.

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Q: (ztan 2 +1) dx – x dy = 0

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Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: dy Given that y = In 9x, find dz dy

A: Use derivative rules to find dy/dx

Q: 30. cos(r + y?) dx dy 32. x²+ y² dx dy 2 y

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Q: dy zsin(x) dz

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Q: y - cx°y' +e + sin(xy) – (ny+ y@) =0 -ху y' =?

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Q: dy 4. = 4 sin 2x ; y = 2, when x = Tt/2 dx

A: Given a differential equation, dydx=4sin2x ; y=2 where x=π2 To find the general solution of the DE.

Q: dy when Find dx x(t) = te', y(t) = 2t + e'. %3D

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Q: Q4/ Evaluate (xy + e") dy dx using Three point formula in x,y-axis and two point formula in z axis

A: You must have an basic idea of double integral to solve this.

Q: y sin (r²) dt

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Q: C. dt² +y" = 0 dy d. xty" + ху" 3 е* e. t2 dt2. t2 ( - t = 1- sint е.

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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.