Match List-I with List-II
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List-I Differential Equation |
List-II Degree |
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(A) $xy\frac{d^2y}{dx^2}+x(\frac{dy}{dx})^2-y\frac{dy}{dx}=0$ |
(I) 3 |
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(B) $\frac{d^2y}{dx^2} +\log (\frac{dy}{dx}=0$ |
(II) 1 |
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(C) $(\frac{d^2y}{dx^2})^2+(\frac{dy}{dx})^3+\frac{dy}{dx}+1=0$ |
(III) not defined |
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(D) $2x^2(\frac{d^2y}{dx^2})^3-5(\frac{dy}{dx})^2+y=0$ |
(IV) 2 |
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)
|
List-I Differential Equation |
List-II Degree |
|
(A) $xy\frac{d^2y}{dx^2}+x(\frac{dy}{dx})^2-y\frac{dy}{dx}=0$ |
(II) 1 |
|
(B) $\frac{d^2y}{dx^2} +\log (\frac{dy}{dx}=0$ |
(III) not defined |
|
(C) $(\frac{d^2y}{dx^2})^2+(\frac{dy}{dx})^3+\frac{dy}{dx}+1=0$ |
(IV) 2 |
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(D) $2x^2(\frac{d^2y}{dx^2})^3-5(\frac{dy}{dx})^2+y=0$ |
(I) 3 |
(A) $x y \frac{d^2y}{dx^2}+x\Big(\frac{dy}{dx}\Big)^2-y\frac{dy}{dx}=0$.
Highest order derivative $\frac{d^2y}{dx^2}$ appears to power $1$. Degree $=1\Rightarrow$(II).
(B) $\frac{d^2y}{dx^2}+\log\!\Big(\frac{dy}{dx}\Big)=0$.
Contains $\log$ of a derivative, not a polynomial in derivatives. Degree not defined $\Rightarrow$(III).
(C) $\Big(\frac{d^2y}{dx^2}\Big)^2+\Big(\frac{dy}{dx}\Big)^3+\frac{dy}{dx}+1=0$.
Highest order derivative $\frac{d^2y}{dx^2}$ occurs with power $2$. Degree $=2\Rightarrow$(IV).
(D) $2x^2\Big(\frac{d^2y}{dx^2}\Big)^3-5\Big(\frac{dy}{dx}\Big)^2+y=0$.
Highest order derivative $\frac{d^2y}{dx^2}$ occurs with power $3$. Degree $=3\Rightarrow$(I).