Which of these differentials is exact? (only one of them is exact) (1 – 2xy)dx + (x² + y²) dy O (22 + y²) dx +(1 – 2æy)dy O (1 – 2æy)dæ + (æ² – y²) dy '(æ² – y²) dx + (1 – 2æy)dy -

Q: 3. | (1- 2x) dx 0.

A: Given that, ∫01xdx=12 ∫01x2dx=13 ∫01x3dx=14 The integral to be evaluated is given as, I=∫011-2x3dx…

Q: 1 Jo (1 + 4xy) dx dy

A:

Q: Let y3 - 4x = 2xy. Find d2y/dx2. Show work please.

A:

Q: g. y = u² + u³, u = ³ - 4v, v = 3 - x², x = 2 u5

A:

Q: 6) Find dy 1+eX for y= dx 1-ex

A:

Q: find dy/dx by implicit differentiation. tan(4x+y)=4x. Use the original equation to simplify your…

A:

Q: Find dy/dx for the following xVx² In y = In + 1 2 (x + 1) 3

A:

Q: Find dy if y=33 dx 09x² 3x² 3 3x² 9 음

A: Solution-

Q: / 11 (2xy- 1) dx + x² dy = 0; (1) = 2

A:

Q: d'y Find dx? 2 y = (2а-3)? dy 48 dx? (2г - 3)" O dy -12 da? (2г- 3)" O d'y 12 dx? (2a-3) dy -8 da?…

A: y=2(2x-3)2

Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

A:

Q: Question 29 Find y' by implicit differentiation for 4x2 y7 - 2x = x+ 4y3. 8xy7+5x++2 y'= 12y2-…

A: Let's find.

Q: (2y3 – x³)dx + 3xy?dy = 0; when x = 1, y = 1 Ans. 5x²y3 = x5 + 4

A:

Q: 2²+2 (Inys

A: Solution:

Q: 2x+1 dx: x+2x+1

A: Given that ∫2x3+1x4+2x+1dx

Q: E. DE with Linear Coefficients (x+2y-1)dx - (2x + 4y + 1)dy = 0

A:

Q: Show that esin(x²)dx < e– 1.

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 2 y = 4х — 3

A:

Q: Differentiate. g(t) =  5 − 7t 8t + 9 g′(t) =

A: solution: the objective is to find the derivative of the given function

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

A:

Q: - 9 dy 8 Find dx for y = (8x - 9) dx ||

A:

Q: dy Find if dx 6x2 + 6y 19 %3D 6x + 3y2

A:

Q: If 3x² + 2xy + y² = 2, then the value of dy/dx at x = 1 is

A: Given that        3x2+2xy+y2= 2 We have to find the value of dy/dx at x=1.

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.