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The differential equation representing the family of curves y2 = 2c(x+√c), where c is a positive perimeter, is of
- a)order 1, degree 3
- b)order 1, degree 2
- c)degree 3 order 3
- d)degree 4 order 4
Correct answer is option 'A'. Can you explain this answer?
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The differential equation representing the family of curves y2= 2c(x+&...
Explanation:
Differential Equation:
- The given family of curves is represented by the equation y^2 = 2c(x + sqrt(c)), where c is a positive parameter.
Order and Degree:
- The order of a differential equation is the highest order derivative present in the equation, while the degree is the power to which this derivative is raised.
- In this case, the derivative with the highest power is the first derivative (y'), making the order of the differential equation 1.
- The degree of the differential equation is determined by the highest power to which this derivative is raised, which in this case is 3 (y'^3).
- Therefore, the differential equation representing the given family of curves is of order 1 and degree 3.
Answer Justification:
- The correct answer is option 'A' (order 1, degree 3) because the given family of curves can be expressed using a differential equation with these characteristics.
- Option 'B' is incorrect as the degree of the differential equation is 3, not 2.
- Option 'C' is incorrect as the order of the differential equation is 1, not 3.
- Option 'D' is incorrect as the degree of the differential equation is 3, not 4.
Therefore, the correct answer is option 'A' (order 1, degree 3).
Differential Equation:
- The given family of curves is represented by the equation y^2 = 2c(x + sqrt(c)), where c is a positive parameter.
Order and Degree:
- The order of a differential equation is the highest order derivative present in the equation, while the degree is the power to which this derivative is raised.
- In this case, the derivative with the highest power is the first derivative (y'), making the order of the differential equation 1.
- The degree of the differential equation is determined by the highest power to which this derivative is raised, which in this case is 3 (y'^3).
- Therefore, the differential equation representing the given family of curves is of order 1 and degree 3.
Answer Justification:
- The correct answer is option 'A' (order 1, degree 3) because the given family of curves can be expressed using a differential equation with these characteristics.
- Option 'B' is incorrect as the degree of the differential equation is 3, not 2.
- Option 'C' is incorrect as the order of the differential equation is 1, not 3.
- Option 'D' is incorrect as the degree of the differential equation is 3, not 4.
Therefore, the correct answer is option 'A' (order 1, degree 3).
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The differential equation representing the family of curves y2= 2c(x+√c), where c is a positive perimeter, is ofa)order 1, degree 3b)order 1, degree 2c)degree 3 order 3d)degree 4 order 4Correct answer is option 'A'. Can you explain this answer?
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