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If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation is
- a)1, 2
- b)2, 1
- c)1, 3
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the general solutions of a differential equation are (y + c)2 = cx,...
There will only one constant in the first-order differential equation. Differentiating the given equation.
Putting the value of c in Eq. (1) and simplifying we will get a first-order and second-degree equation. Hence, (A) is the correct answer.
Most Upvoted Answer
If the general solutions of a differential equation are (y + c)2 = cx,...
To determine the order and degree of a differential equation, we need to analyze the given general solution. Let's break down the given general solution step by step:
General solution: (y - c)^2 = cx
1. Expanding the equation:
y^2 - 2cy + c^2 = cx
2. Rearranging the terms:
y^2 - 2cy - cx + c^2 = 0
Now, let's analyze the equation to determine its order and degree.
Order of a Differential Equation:
The order of a differential equation is determined by the highest derivative present in the equation. In this case, we don't see any derivatives explicitly mentioned in the general solution. However, we can rewrite the equation in differential form:
dy/dx = (2cy - c^2 + cx)/x
Here, we have the first derivative dy/dx present. Hence, the order of the differential equation is 1.
Degree of a Differential Equation:
The degree of a differential equation is determined by the highest power of the highest derivative present in the equation. In this case, we can see that the highest power of the highest derivative (dy/dx) is 1. However, we also have the term y^2 present in the equation.
To handle this situation, we can express y^2 as (dy/dx)^2 and rewrite the equation as:
(dy/dx)^2 - 2cy - cx + c^2 = 0
Now, we can see that the highest power of the highest derivative is 2, which corresponds to the quadratic term (dy/dx)^2. Hence, the degree of the differential equation is 2.
Therefore, the order and degree of the given differential equation are 1 and 2, respectively. Hence, the correct answer is option A) 1, 2.
General solution: (y - c)^2 = cx
1. Expanding the equation:
y^2 - 2cy + c^2 = cx
2. Rearranging the terms:
y^2 - 2cy - cx + c^2 = 0
Now, let's analyze the equation to determine its order and degree.
Order of a Differential Equation:
The order of a differential equation is determined by the highest derivative present in the equation. In this case, we don't see any derivatives explicitly mentioned in the general solution. However, we can rewrite the equation in differential form:
dy/dx = (2cy - c^2 + cx)/x
Here, we have the first derivative dy/dx present. Hence, the order of the differential equation is 1.
Degree of a Differential Equation:
The degree of a differential equation is determined by the highest power of the highest derivative present in the equation. In this case, we can see that the highest power of the highest derivative (dy/dx) is 1. However, we also have the term y^2 present in the equation.
To handle this situation, we can express y^2 as (dy/dx)^2 and rewrite the equation as:
(dy/dx)^2 - 2cy - cx + c^2 = 0
Now, we can see that the highest power of the highest derivative is 2, which corresponds to the quadratic term (dy/dx)^2. Hence, the degree of the differential equation is 2.
Therefore, the order and degree of the given differential equation are 1 and 2, respectively. Hence, the correct answer is option A) 1, 2.
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Community Answer
If the general solutions of a differential equation are (y + c)2 = cx,...
There will only one constant in the first-order differential equation. Differentiating the given equation.
Putting the value of c in Eq. (1) and simplifying we will get a first-order and second-degree equation. Hence, (A) is the correct answer.
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