Match the slope field to the appropriate ODE dy 1. = x – y dx dy 2. = x + y dx 3. dx dy a2 – y dy A. dæ

Q: x*y – xy³ = –2 ху

A: Consider: x4y-xy3=-2. Evaluate dydx. Apply implicit differentiation by derivating both side of…

Q: dy dx y = 2log 6X Find

A: Given that y=2 log6x Derive w.r.t 'x' dydx=ddx2log6xdydx=2xlog 6 Since ddxlogax=1x log a

Q: dy 3. Find dx? .2, Given that xy + x²y° = 5.

A:

Q: dy Find • for the function y =23x dx

A: The objective of the question is to find the derivative of the function y = 23x with respect to x.…

Q: dy If x= y1- y² , find dx X = y•

A:

Q: d y. d3y dy d'y dy (+() dy + y dt2" dt + b dt dt2 ay dt3 d/dt (5 %3D dt

A: Explained below

Q: Find the second derivative, Select the correct answer below: d² 9x² dx² y³ d²y 7.3 dx² 3y³ d²y dx²…

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Q: dy Find for y = dx /9 – x4 dy dx

A:

Q: dy Find if dx V(2? + 7) 5. 3 dy %3D

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Q: d²y d²y dy + d dt. d dy dy = ay + by dt dt. dt dt2 dt2 dt

A: We find the value of a,b,c and d.

Q: Use implicit differentiation to find dy/dx. e3x = sin(x + 8y) %3D Select one: O A. dy -3eX %3D dx…

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Q: dy = x*y² +y dx Find y for

A:

Q: Consider the function g(x): y = x² • V3- 2x. a) State the domain of the function. dy b) Determine dx…

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Q: Find dy: 5x³ =-3xy + 2 dx ****

A: To find the derivative

Q: 2 -e dy=x(xdy-ydx).

A:

Q: 2 x If y = x¯e" sinx,Find d

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Q: find 5x² then find dy in terms of x and y. X If 3y - xy = 5x² then

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Q: cot x B5. Find- dx for the function y = 1+ cot x

A: Solution:-

Q: dy The derivative for the function dx y = cot¬l V4 – x²

A:

Q: dy Find using implicit differentiation, for the equation x+ y° = 10 is. dx %3D x2 y? x?

A:

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.