Solve the given differential equation by separation of variables. ху + 5х — у —5 ху — 2х + бу-12 We first factorize dx ху + 5х — у — 53(х+| —1 )(y+ 5 ху — 2х + бу — 12-(х+| 6 )(y+-2 ソー2 ア+5 х —1 And then we separate the variables dy= dx x +6 The solution to the differential equation is

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Q: How do you solve this using differential equations?

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Q: can you give an example in real life, where differential equations are applied?

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Q: 200x + 250y D44,000 x+y= 200 %3D 44.000

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Q: (10x-19) (3r + 2) (5x-3)

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Q: Solve (x-1)' +(x-2)'+(x - 3)' +(x + 4)' +(x + 5)' = 0

A: The solution for the above question is as shown below.

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Q: x3y'''+2x2y''-2xy'=2x-4 Find the general solution of the equation.

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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.