Match List-I with List-II
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List-I |
List-II |
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(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{dy}{dx}\right)$ |
(I) 4 |
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(B) The degree of differential equation $\frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^{1/4}+x^{1/5}=0$ |
(II) 1 |
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(C) The degree of differential equation $\frac{d^2y}{dx^2}\left(\frac{dy}{dx}\right)^3+6y^5=0$ |
(III) Not defined |
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(D) The degree of differential equation $1+\left(\frac{dy}{dx}\right)^4=7\left(\frac{d^2y}{dx^2}\right)^3$ |
(IV) 3 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
Explanation:
Matching List-I with List-II:
(A) The degree of the differential equation
$ \left( \frac{d^2 y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin\left( \frac{dy}{dx} \right) $
→ Highest order derivative is $ \frac{d^2 y}{dx^2} $ raised to power 2, and the equation is polynomial in derivatives.
→ Degree = 2 but RHS involves $ \sin\left( \frac{dy}{dx} \right) $, so it is not polynomial in derivatives.
→ Degree is Not defined ⇒ (III)
(B) $ \frac{d^2 y}{dx^2} + \left( \frac{dy}{dx} \right)^{1/4} + x^{1/5} = 0 $
→ $\frac{dy}{dx} =( \frac{d^2 y}{dx^2}+ x^{1/5})^{4}$
→ Degree is 4 since $ \frac{d^2 y}{dx^2} $ degree is 4 → (I)
(C) $ \frac{d^2 y}{dx^2} \left( \frac{dy}{dx} \right)^3 + 6y^5 = 0 $
→ Highest derivative: $ \frac{d^2 y}{dx^2} $ raised to power 1 and equation is polynomial
→ Degree = 1 ⇒ (II)
(D) $ 1 + \left( \frac{dy}{dx} \right)^4 = 7 \left( \frac{d^2 y}{dx^2} \right)^3 $
→ Highest derivative: $ \frac{d^2 y}{dx^2} $ raised to power 3
→ Degree = 3 ⇒ (IV)