Match List-I with List-II
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List-I (Differential equation) |
List-II (Order and Degree) |
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(A) $\frac{d^3y}{dx^3} + y^2+e^{dy/dx} = 0$ |
(I) order = 3, degree = 1 |
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(B) $\left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}+1=0$ |
(II) order = 3, degree not defined |
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(C) $2x^2\frac{d^2y}{dx^2}-3\left(\frac{dy}{dx}\right)^2+y=0$ |
(III) order = 2, degree = 3 |
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(D) $\frac{d^3y}{dx^3} +2\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}=0$ |
(IV) order = 2, degree = 1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
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List-I (Differential equation) |
List-II (Order and Degree) |
|
(A) $\frac{d^3y}{dx^3} + y^2+e^{dy/dx} = 0$ |
(II) order = 3, degree not defined |
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(B) $\left(\frac{d^2y}{dx^2}\right)^3+\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}+1=0$ |
(III) order = 2, degree = 3 |
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(C) $2x^2\frac{d^2y}{dx^2}-3\left(\frac{dy}{dx}\right)^2+y=0$ |
(IV) order = 2, degree = 1 |
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(D) $\frac{d^3y}{dx^3} +2\left(\frac{dy}{dx}\right)^2+\frac{dy}{dx}=0$ |
(I) order = 3, degree = 1 |
Analyze each differential equation for order and degree:
(A) $\frac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 0$
Contains exponential of derivative ⇒ degree is not defined
Highest order derivative = third order
⇒ (A) → (II)
(B) $\left( \frac{d^2y}{dx^2} \right)^3 + \left( \frac{dy}{dx} \right)^2 + \frac{dy}{dx} + 1 = 0$
Highest order = 2, and highest power = 3
⇒ (B) → (III)
(C) $2x^2 \frac{d^2y}{dx^2} - 3\left( \frac{dy}{dx} \right)^2 + y = 0$
Highest order = 2, and degree = 1 (since no non-integer powers or functions of derivative)
⇒ (C) → (IV)
(D) $\frac{d^3y}{dx^3} + 2\left( \frac{dy}{dx} \right)^2 + \frac{dy}{dx} = 0$
Highest order = 3, highest power = 1 (since highest derivative appears linearly)
⇒ (D) → (I)