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The differential equation whose solution is Ax2 + By2 = 1, where A and B are arbitrary constants, is of
- a)second order and first degree
- b)first order and second degree
- c)first order and first degree
- d)second order and second degree
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The differential equation whose solution is Ax2 + By2 = 1, where A and...
Ax^2 + By^2 = 1
diff both sides w. r. t. x :-
2Ax + 2By y' = 0
Ax + By y' = 0
Ax = -By y'
-A/B = y y' / x
diff both sides w.r.t. x :-
((y y'' + (y')^2 ) x - y y')/x^2 = 0
x y y" + (y')^2 x - y y' = 0
Here we can see that :-
Order = 2 and degree = 1
Thus we can say that the option (A) is correct
diff both sides w. r. t. x :-
2Ax + 2By y' = 0
Ax + By y' = 0
Ax = -By y'
-A/B = y y' / x
diff both sides w.r.t. x :-
((y y'' + (y')^2 ) x - y y')/x^2 = 0
x y y" + (y')^2 x - y y' = 0
Here we can see that :-
Order = 2 and degree = 1
Thus we can say that the option (A) is correct
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Community Answer
The differential equation whose solution is Ax2 + By2 = 1, where A and...
To determine the order and degree of a differential equation, we need to analyze the highest order derivative and the highest power of that derivative in the equation. Let's break down the given equation and analyze it step by step.
Given differential equation: Ax^2 - By^2 = 1
1. Separating the variables:
To begin, we need to separate the variables. In this case, we have two variables, x and y. We can rearrange the equation to isolate the variables on different sides:
Ax^2 - By^2 = 1
Ax^2 = 1 + By^2
2. Taking derivatives:
Next, let's take the derivatives of both sides of the equation. The order of the derivative is determined by the highest derivative present in the equation.
d/dx (Ax^2) = d/dx (1 + By^2)
Differentiating the left side with respect to x gives:
2Ax = 0
Differentiating the right side with respect to x gives:
0 = 0
3. Analyzing the order and degree:
From the derivatives obtained, we can see that the highest order derivative is the first derivative (d/dx) and it appears only once in the equation. Therefore, the order of the differential equation is first order.
Now, let's analyze the degree of the differential equation. The degree is determined by the highest power of the highest order derivative. In this case, the highest power of the first derivative is 1. Therefore, the degree of the differential equation is first degree.
Hence, the correct answer is option 'A' - the given differential equation is of first order and first degree.
Given differential equation: Ax^2 - By^2 = 1
1. Separating the variables:
To begin, we need to separate the variables. In this case, we have two variables, x and y. We can rearrange the equation to isolate the variables on different sides:
Ax^2 - By^2 = 1
Ax^2 = 1 + By^2
2. Taking derivatives:
Next, let's take the derivatives of both sides of the equation. The order of the derivative is determined by the highest derivative present in the equation.
d/dx (Ax^2) = d/dx (1 + By^2)
Differentiating the left side with respect to x gives:
2Ax = 0
Differentiating the right side with respect to x gives:
0 = 0
3. Analyzing the order and degree:
From the derivatives obtained, we can see that the highest order derivative is the first derivative (d/dx) and it appears only once in the equation. Therefore, the order of the differential equation is first order.
Now, let's analyze the degree of the differential equation. The degree is determined by the highest power of the highest order derivative. In this case, the highest power of the first derivative is 1. Therefore, the degree of the differential equation is first degree.
Hence, the correct answer is option 'A' - the given differential equation is of first order and first degree.
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The differential equation whose solution is Ax2 + By2 = 1, where A and B are arbitrary constants, is ofa)second order and first degreeb)first order and second degreec)first order and first degreed)second order and second degreeCorrect answer is option 'A'. Can you explain this answer?
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