Match List-I with List-II
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List-I Differential Equation |
List-II Degree |
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(A) $\frac{d^2y}{dx^2} +\sqrt{\frac{dy}{dx}}-y=0$ |
(I) 6 |
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(B) $\sqrt{\frac{d^3y}{dx^3}}-\sqrt[12]{\frac{d^2y}{dx^2}}=0$ |
(II) Not defined |
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(C) $\left(\frac{d^2y}{dx^2}\right)^2+\frac{dy}{dx}+e^{\frac{dy}{dx}}=x^2$ |
(III) 3 |
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(D) $\sqrt[3]{\frac{dy}{dx}}-\frac{d^2y}{dx^2}=e^x$ |
(IV) 2 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
|
List-I Differential Equation |
List-II Degree |
|
(A) $\frac{d^2y}{dx^2} +\sqrt{\frac{dy}{dx}}-y=0$ |
(IV) 2 |
|
(B) $\sqrt{\frac{d^3y}{dx^3}}-\sqrt[12]{\frac{d^2y}{dx^2}}=0$ |
(I) 6 |
|
(C) $\left(\frac{d^2y}{dx^2}\right)^2+\frac{dy}{dx}+e^{\frac{dy}{dx}}=x^2$ |
(II) Not defined |
|
(D) $\sqrt[3]{\frac{dy}{dx}}-\frac{d^2y}{dx^2}=e^x$ |
(III) 3 |
(A) $\frac{d^2y}{dx^2}+\sqrt{\frac{dy}{dx}}-y=0$
Square both sides after isolating radical
$\sqrt{\frac{dy}{dx}}=y-\frac{d^2y}{dx^2}$
$\frac{dy}{dx}=\left(y-\frac{d^2y}{dx^2}\right)^2$
Highest order derivative is $\frac{d^2y}{dx^2}$ and its power is $2$
$(A)\rightarrow(IV)$
(B) $\sqrt{\frac{d^3y}{dx^3}}-\sqrt[12]{\frac{d^2y}{dx^2}}=0$
$\sqrt{\frac{d^3y}{dx^3}}=\sqrt[12]{\frac{d^2y}{dx^2}}$
Raise both sides to power $12$
$\left(\frac{d^3y}{dx^3}\right)^6=\frac{d^2y}{dx^2}$
Highest order derivative is $\frac{d^3y}{dx^3}$ with power $6$
$(B)\rightarrow(I)$
(C) $\left(\frac{d^2y}{dx^2}\right)^2+\frac{dy}{dx}+e^{\frac{dy}{dx}}=x^2$
Contains exponential of derivative, cannot be made polynomial in derivatives
Degree is not defined
$(C)\rightarrow(II)$
(D) $\sqrt[3]{\frac{dy}{dx}}-\frac{d^2y}{dx^2}=e^x$
$\sqrt[3]{\frac{dy}{dx}}=\frac{d^2y}{dx^2}+e^x$
Cube both sides
$\frac{dy}{dx}=\left(\frac{d^2y}{dx^2}+e^x\right)^3$
Highest order derivative is $\frac{d^2y}{dx^2}$ with power $3$
$(D)\rightarrow(III)$
Final Matching: (A)-(IV), (B)-(I), (C)-(II), (D)-(III).