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Form the differential equation representing the family of curves y = mx where m is arbitrary constant. |
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Answer» The given family of curves represents the equation of straight lines. ∴ y = mx ………. (1) Differentiate w.r.t x, we get dy dy/dx = m ∴ substitute m = dy/dx, we have y = mx ⇒ y = dy/dx x dy/dx = y/x dy/dx - y/x = 0 which is the required differential equation. |
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