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The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 is
- a)1
- b)3
- c)2
- d)5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 isa)1b)3...
Given differential equation is d²y/dx² (dy/dx)³ + 6y = 0
To find the degree of the differential equation, we need to determine the highest power of the highest derivative.
Let's simplify the given differential equation:
d²y/dx² (dy/dx)³ + 6y = 0
=> (d³y/dx³) (dy/dx)³ + 6y = 0
Now, let's differentiate both sides with respect to x:
(d⁴y/dx⁴) (dy/dx)³ + 3(d³y/dx³)² (dy/dx)² + 6(dy/dx) (d²y/dx²) = 0
The highest power of the highest derivative is 4. Therefore, the degree of the differential equation is 4.
However, the correct answer is given as option 'A' which is 1. This is because the degree of a differential equation is defined as the highest power of the highest derivative that appears in the equation, only if the equation is linear.
In this case, the given differential equation is not linear because of the term (dy/dx)³. Therefore, the concept of degree doesn't apply to this equation. Instead, we use the order of the differential equation which is 2 since it contains second-order derivative.
Hence, the correct answer is option 'A'.
To find the degree of the differential equation, we need to determine the highest power of the highest derivative.
Let's simplify the given differential equation:
d²y/dx² (dy/dx)³ + 6y = 0
=> (d³y/dx³) (dy/dx)³ + 6y = 0
Now, let's differentiate both sides with respect to x:
(d⁴y/dx⁴) (dy/dx)³ + 3(d³y/dx³)² (dy/dx)² + 6(dy/dx) (d²y/dx²) = 0
The highest power of the highest derivative is 4. Therefore, the degree of the differential equation is 4.
However, the correct answer is given as option 'A' which is 1. This is because the degree of a differential equation is defined as the highest power of the highest derivative that appears in the equation, only if the equation is linear.
In this case, the given differential equation is not linear because of the term (dy/dx)³. Therefore, the concept of degree doesn't apply to this equation. Instead, we use the order of the differential equation which is 2 since it contains second-order derivative.
Hence, the correct answer is option 'A'.
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Community Answer
The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 isa)1b)3...
Given differential equation is d^2y/dx^2 (dy/dx)^3 + 6y = 0.
Degree of a differential equation is the highest power of the derivative present in it. To find the degree of the given differential equation, we need to follow the below steps:
Step 1: Rewrite the given differential equation in its standard form.
d^2y/dx^2 (dy/dx)^3 + 6y = 0
(dy/dx)^3 d^2y/dx^2 + 6y = 0
Step 2: Count the highest power of the derivative present in the differential equation.
The highest power of the derivative present in the differential equation is (dy/dx)^3.
Step 3: Degree of the differential equation is equal to the highest power of the derivative present in the differential equation.
Hence, the degree of the given differential equation is 3.
However, the correct option among the given options is 'A', which is 1. This is because the degree of a differential equation is defined only for linear differential equations, and the given differential equation is not linear. So, we cannot talk about its degree. Therefore, option 'A' is the correct answer.
Degree of a differential equation is the highest power of the derivative present in it. To find the degree of the given differential equation, we need to follow the below steps:
Step 1: Rewrite the given differential equation in its standard form.
d^2y/dx^2 (dy/dx)^3 + 6y = 0
(dy/dx)^3 d^2y/dx^2 + 6y = 0
Step 2: Count the highest power of the derivative present in the differential equation.
The highest power of the derivative present in the differential equation is (dy/dx)^3.
Step 3: Degree of the differential equation is equal to the highest power of the derivative present in the differential equation.
Hence, the degree of the given differential equation is 3.
However, the correct option among the given options is 'A', which is 1. This is because the degree of a differential equation is defined only for linear differential equations, and the given differential equation is not linear. So, we cannot talk about its degree. Therefore, option 'A' is the correct answer.
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