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Question
Find the differential equation representing the curve y = cx + c2.
Solution
The equation of the given curve is
y = cx + c2 .....(1)
Differentiating both side of (1) with respect to x, we get
`dy/dx=c `
Substituting `c=dy/dx` in (1), we get
`y=x dy/dx+(dy/dx)^2`
`=>(dy/dx)^2+x dy/dx−y=0`
This is the differential equation, which is representing the given curve.
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