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What are the order and degree respectively of the differential equation whose solution is y = cx + c2 - 3c3/2 + 2, where c is a parameter?
- a)1,2
- b)2,2
- c)1,3
- d)1,4
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
What are the order and degree respectively of the differential equatio...
Given:
Solution of differential equation is
y - cx + c2 - 3c3/2 + 2 ...........(1)
To find order and degree of differential equation, we will find differential equation first.
Now differentiating equation (1) w.r.t. x and putting value of c to remove it, we get
Hence order of differential equation is 1 and degree is 4.
Solution of differential equation is
y - cx + c2 - 3c3/2 + 2 ...........(1)
To find order and degree of differential equation, we will find differential equation first.
Now differentiating equation (1) w.r.t. x and putting value of c to remove it, we get
Hence order of differential equation is 1 and degree is 4.
Most Upvoted Answer
What are the order and degree respectively of the differential equatio...
Order and Degree of Differential Equation
Order and degree of a differential equation refer to the highest derivative and the highest power of the derivative in the equation, respectively.
Solution of the Differential Equation
The given solution is y = cx^2 - 3c^3/2.
Differentiating with respect to x, we get:
dy/dx = 2cx - (9/2)c^3/2
Differentiating again, we get:
d2y/dx2 = 2c - (9/4)c^3/2
Substituting the values in the differential equation:
d2y/dx2 - 3dy/dx + 2y = 0
We get:
(2c - (9/4)c^3/2) - 3(2cx - (9/2)c^3/2) + 2(cx^2 - 3c^3/2) = 0
Simplifying the expression, we get:
(-5c^2/2)x^2 + (12c^3/2)x - 5c^4/4 = 0
Comparing this with the standard form of a quadratic equation:
ax^2 + bx + c = 0
We get:
a = -5c^2/2
b = 12c^3/2
c = -5c^4/4
Degree and Order of the Differential Equation
The degree of the differential equation is the highest power of the derivative in the equation. In this case, the highest power of the derivative is 2. Therefore, the degree of the differential equation is 2.
The order of the differential equation is the highest order of the derivative in the equation. In this case, the highest order of the derivative is also 2. Therefore, the order of the differential equation is 2.
Hence, the correct option is (D) 1, 4.
Order and degree of a differential equation refer to the highest derivative and the highest power of the derivative in the equation, respectively.
Solution of the Differential Equation
The given solution is y = cx^2 - 3c^3/2.
Differentiating with respect to x, we get:
dy/dx = 2cx - (9/2)c^3/2
Differentiating again, we get:
d2y/dx2 = 2c - (9/4)c^3/2
Substituting the values in the differential equation:
d2y/dx2 - 3dy/dx + 2y = 0
We get:
(2c - (9/4)c^3/2) - 3(2cx - (9/2)c^3/2) + 2(cx^2 - 3c^3/2) = 0
Simplifying the expression, we get:
(-5c^2/2)x^2 + (12c^3/2)x - 5c^4/4 = 0
Comparing this with the standard form of a quadratic equation:
ax^2 + bx + c = 0
We get:
a = -5c^2/2
b = 12c^3/2
c = -5c^4/4
Degree and Order of the Differential Equation
The degree of the differential equation is the highest power of the derivative in the equation. In this case, the highest power of the derivative is 2. Therefore, the degree of the differential equation is 2.
The order of the differential equation is the highest order of the derivative in the equation. In this case, the highest order of the derivative is also 2. Therefore, the order of the differential equation is 2.
Hence, the correct option is (D) 1, 4.
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What are the order and degree respectively of the differential equation whose solution is y = cx + c2 - 3c3/2 + 2, where c is a parameter?a)1,2b)2,2c)1,3d)1,4Correct answer is option 'D'. Can you explain this answer?
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