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

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Q: Exercise 2. Integrate the following functions. 1. S(3x+2)°dz 2. 3.

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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 Find for the function y = 11*.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Determine dy for y=VX2+1 . dx2 alx

A: Obtain the second derivative as follows.

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

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Q: dy If x= y1- y² , find dx X = y•

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Q: 5. - y = e*y? dx

A: Given, dydx-y=exy2 To solve the above Differential equation.

Q: 1. xyz dx dy dz

A: There is triple integration. First we integrate with respect to x, then w.r.t y and then w.r.t z.

Q: dy Given the function y = f(x) = sin(3x+ 4y). Determine dx %3D

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Q: 7. (x+ ycot) dy – ydx = 0. 8. (xy + y²)dx = (x² + xy + y²)dy. 0. %3D | %3D

A: We have to solve the following differential equation

Q: 2 x If y = x¯e" sinx,Find d

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Q: dy EX.8: Find for the following functions: dx 1) y = ( x²+ 1)5

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Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

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Q: dy d {-3xy} in terms of x , y , and dx y is a differentiable function of x . Write dx

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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.