6) The variables x and y satisfy the differential equation X = y(1-2x²), dx and it is given that y = 2 when x = 1. Solve the differential equation and obtain an expression for y in terms of x.

Q: Determine the differential equation that is satisfied x2 + y2 + 2ax + 2by + c = 0

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Q: (бх + у?)dх + y(2х — Зу)dy %3D 0

A: We have to solve given problem:

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Q: 3y (11) dx* 6x2

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: The solution of the differential equation (x³ + 3xy?)dx+ (y³+3x²y)dy=D0 is

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Q: What is the general solution ti the differential equation (x-4y-9)dx+(4x+y-2)dy=0 ?

A: Given: x-4y-9dx+4x+y-2dy=0

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Q: dу ху+2у- х-2 dx xy- 3y+ x-3

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Q: D=d/dx to be  (4D4-8D3-7D2+11D+6)y=0    solve the differential equatio

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Q: What does it mean for a function to be a solution to a differential equation?

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Q: Solve the differential equation: (D² + 1)y = tan x

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Q: Uxx - Uxy = = 0

A: Here I am solving the last question ; as per problem-solving guidelines, we will be solving one…