Match List-I with List-II
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List-I Differential Equation |
List-II Sum of order and degree |
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(A) $\frac{d^2y}{dx^2}+\frac{dy}{dx} +3y= \sin x$ |
(I) 2 |
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(B) $\frac{dy}{dx}=\sin (x + y)$ |
(II) 3 |
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(C) $\sqrt{1+(\frac{dy}{dx})^2}=\frac{d^2y}{dx^2}$ |
(III) 4 |
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(D) $x^2(\frac{d^2y}{dx^2})^3+(\frac{dy}{dx})^4+ y^3 = 0$ |
(IV) 5 |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(I), (C)-(III), (D)-(IV) **
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List-I Differential Equation |
List-II Sum of order and degree |
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(A) $\frac{d^2y}{dx^2}+\frac{dy}{dx} +3y= \sin x$ |
(II) 3 |
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(B) $\frac{dy}{dx}=\sin (x + y)$ |
(I) 2 |
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(C) $\sqrt{1+(\frac{dy}{dx})^2}=\frac{d^2y}{dx^2}$ |
(IV) 5 |
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(D) $x^2(\frac{d^2y}{dx^2})^3+(\frac{dy}{dx})^4+ y^3 = 0$ |
(III) 4 |
(A) $\frac{d^{2}y}{dx^{2}}+\frac{dy}{dx}+3y=\sin x$ → order $2$, degree $1$ → sum $3$ → (II)
(B) $\frac{dy}{dx}=\sin(x+y)$ → order $1$, degree $1$ → sum $2$ → (I)
(C) $\sqrt{\,1+\left(\frac{dy}{dx}\right)^{2}\,}=\frac{d^{2}y}{dx^{2}}$ Square: $1+\left(\frac{dy}{dx}\right)^{2}=\left(\frac{d^{2}y}{dx^{2}}\right)^{2}$ → order $2$, degree $2$ → sum $4$ → (III)
(D) $x^{2}\left(\frac{d^{2}y}{dx^{2}}\right)^{3}+\left(\frac{dy}{dx}\right)^{4}+y^{3}=0$ Order $2$, degree $3$ → sum $5$ → (IV)
Correct matching: (A)→(II), (B)→(I), (C)→(III), (D)→(IV)