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The differential equation representing the family of circles touching y-axis at origin is:
- a)Linear & of first order
- b)Linear & of second order
- c)Non-linear & of first order
- d)Non-linear & of second order
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The differential equation representing the family of circles touching ...
Equation of circle having centre at (r, 0) and radius r is written as:
(x - r)2 + (y - 0)2 = r2
(x - r)2 + (y - 0)2 = r2
x2 + r2 - 2xr + y2 = r2
x2 - 2xr + y2 = 0
x2 + y2 = 2xr ___(1)
Differentiating on both sides:
x + yy’ = r
Put value of r in equation (1):
Thus, x2 + y2 = 2 (x + yy’) x
2xyy’ + x2 - y2 = 0
Note:
A differential equation is said to be linear if the dependent variable and its derivative appears in first degree.
Note:
is the first order linear differential equation.
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The differential equation representing the family of circles touching y-axis at origin is:a)Linear & of first orderb)Linear & of second orderc)Non-linear & of first orderd)Non-linear & of second orderCorrect answer is option 'C'. Can you explain this answer?
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