Match List I with List II with regard to degree of the Differential Equation.
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LIST I |
LIST II |
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A. $\frac{d^3 y}{d x^3}+\sin y=0$ |
I. 4 |
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B. $\left(\frac{d y}{d x}\right)^4+\cos \left(\frac{d y}{d x}\right)-1=0$ |
II. 1 |
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C. $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^4=0$ |
III. Not defined |
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D. $\left(\frac{d^2 y}{d x^2}\right)^5+2\left(\frac{d^3 y}{d x^3}\right)^4+7=0$ |
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
Degree of a differential equation is defined only when the equation is a polynomial in derivatives.
(A) $\frac{d^{3}y}{dx^{3}}+\sin y=0$
Highest order derivative $\frac{d^{3}y}{dx^{3}}$ appears to power $1$.
Degree $=1$.
So (A) → (II).
(B) $\left(\frac{dy}{dx}\right)^{4}+\cos\left(\frac{dy}{dx}\right)-1=0$
Derivative appears inside $\cos$, so not a polynomial in derivatives.
Degree is not defined.
So (B) → (III).
(C) $\left(\frac{d^{2}y}{dx^{2}}\right)^{2}+\left(\frac{dy}{dx}\right)^{4}=0$
Highest order derivative is $\frac{d^{2}y}{dx^{2}}$ and its power is $2$.
Degree $=2$.
So (C) → (IV).
(D) $\left(\frac{d^{2}y}{dx^{2}}\right)^{5}+2\left(\frac{d^{3}y}{dx^{3}}\right)^{4}+7=0$
Highest order derivative is $\frac{d^{3}y}{dx^{3}}$ and its power is $4$.
Degree $=4$.
So (D) → (I).
final answer: (A)–(II), (B)–(III), (C)–(IV), (D)–(I)