Match List-I with List-II

List-I	List-II
(A) Degree of the differential equation $\frac{d^2y}{dx^2} = e^{dy/dx}$ is	(I) 2
(B) Order of the differential equation $(\frac{dy}{dx})^2 + \frac{d^3y}{dx^3} = 0$ is	(II) not defined
(C) Degree of the differential equation $\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 - 5x^2 = 0$	(III) 3
(D) If p is the order and q is the degree of the differential equation $\frac{dy}{dx} + 3y = e^x$, then p + q is	(IV) 1

Choose the correct answer from the options given below:

Order of a differential equation is determined by the highest derivative present.

Degree of a differential equation is the power of the highest order derivative when the equation is polynomial in all derivatives. If the equation is not polynomial in derivatives, the degree is not defined.

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For (A): $\frac{d^2y}{dx^2} = e^{dy/dx}$

The first derivative $\frac{dy}{dx}$ appears inside an exponential function.

The equation cannot be expressed as a polynomial in derivatives.

Degree is not defined → (II)

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For (B): $(\frac{dy}{dx})^2 + \frac{d^3y}{dx^3} = 0$

The derivatives present are $\frac{dy}{dx}$ and $\frac{d^3y}{dx^3}$.

The highest order derivative is $\frac{d^3y}{dx^3}$.

Order is 3 → (III)

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For (C): $\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 - 5x^2 = 0$

The highest order derivative is $\frac{d^2y}{dx^2}$.

The equation is polynomial in all derivatives.

The power of $\frac{d^2y}{dx^2}$ is 1.

Degree is 1 → (IV)

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For (D): $\frac{dy}{dx} + 3y = e^x$

The highest order derivative is $\frac{dy}{dx}$.

Order $p = 1$

The equation is polynomial in derivatives, and the power of $\frac{dy}{dx}$ is 1.

Degree $q = 1$

$p + q = 1 + 1 = 2$ → (I)

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Final Matching:

(A) → (II)

(B) → (III)

(C) → (IV)

(D) → (I)