x2-y2 dy 8. dx du Y: Formula: J Ta?-u² = sin-1 u V a

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

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Q: N3xy -y,whtre x sint and y =e. find dwl dt whin

A: w=x2y-y2x=sin ty=et

Q: dy +y = sin (;) cos t, %3D dt2

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Q: Q.1B) Solve the follwing diferential equation: 1 dy x dx siny + ycosy 2logx +1

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Q: Q) Lind d/dx of ® xe 1o x+3J = 0 2 2sinx cos y =1 ® x -se cs

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

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

A: Differentiation

Q: Given z = 64 sint+ 5 and y = 64 cos t + 4 da (i) dt dy (ii) dt dy (iii) dx || ||

A: Using derivatives of parametric function.

Q: dy 28. (i) Find , where a) y= In b) x+y+ cosxy = 0 dy (ii) Given that x= e'cost and y=e'sint, find 2…

A: As per the guidelines we can solve the first three subparts or first one question. If you want more…

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: d'y Calculate y = eX + e* dy %3D dx2

A: It is known that if  we have a function f(ax) then the derivative of the function is,   Here it is…

Q: Given x 13t - 12 and y = 169 sin t %3D %3D dy %3D dx dy dæ?

A: Given that       x = 13t - 12   and   y = 169 sin t Here we have to calculate     dy/dx         and…

Q: Solve the I.V.P using [x = zry]. y di dx + (y cos ( 1 ) - x) dy = 0, y (0) = 262

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

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Q: d²i di 1 d. +R- +-i= E@cos ot dt? dt C a'v a'v ôy = 0 е. ôx

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Q: Given a = 40 sint + 12 and y = 40 cos t + 29 da (i) dt dy (ii) dt %3D dy (iii) dx ||

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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: dy_2y 1. Verify that x'sinx is a solution of -2-y = y cot x dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: I 1 y sin(2²)dx dy. 0. y2

A: See the details solution in below

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: 11. dw 12. J(Gu - 1)(3u* + 2) du J-scos z + 4 sec" x) dx 13.

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Q: Q2- : Classify and Solve; d?y + 9: dt dy cos? t + cosht + sinh t + sin? t +3 sin t - 3t %3D dt?

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Q: dy sin(4x) Find for y dz V1 - x4 dy de

A: The given expression is y=sin(4x)1-x4. Find the derivative of the expression. The quotient rule of…

Q: dy cos(x +y), when x = 0,y == dx

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

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Q: (x – y* + y? sin )dx - (3xy + 2y cos r)dy subject to initial condition y(0) = 1 (M

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Q: Solve for if y- Ina 2- y?. da MCQ3.pdf dy 2y +1 dx dy 2y +1 dx dy dæ -(2y+1)x 1 dy (2y+ 1)a TERIRS…

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Q: e^(x)cos(y)=1+sin(xy) dy/dx?

A: To differentiate :

Q: (a) Find the differential dy. y = V 24 + x2 dy = V 24 +x?

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Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: d’y ,dy -2+5y = e" cos 2x b) t dt dt

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Q: Given x = 70 sint + 13 and y = 70 cos t+ 22 dx (i) dt %3D dy (ii) dt dy (iii) -

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Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: d'y dx di y (x,0)=sin Tx ,t=0,0 ≤ x ≤l 8 dy (x,0) Solve the equation and with y (0,1)=y (1,r) = 0…

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Q: (e* – sin y) dx + cos y dy = 0; when x = 0,y = 1 - %3D

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

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Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: dx Reduce the given DE into Bernoulli's equation: = 3x³y? y dy +

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Q: dy Find -5 y%3D(2+cos4t) dy dt

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

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Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: 2). ſ y cos(y) sin² (v) dy

A: Given: ∫ycosysin2ydy

Q: xy dnt (y +De dy =0 answer: 2.) x dx answer: (y- cas cosx dy = O

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Q: y.cos(z) dx dy dz * 0 0

A: Given that: ∫01∫0π∫0πy.coszdxdydz

Q: y sin (r²) dt

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Q: :- Janx sinx+1 dt = 4 – y? b) Solve to Find if ay cscx – есх dt = xy Q3.a) Find if y + JE sint+1 dx

A: Solve: cscx-∫tanxxy1sinx+1dt=4-y2 y+∫xsecx1sint+1dt=xy