# Which of the following represents a second order differential equation? Option 1) $\frac{\mathrm{d} y}{\mathrm{d} x} = \ln x$ Option 2) $\frac{\mathrm{d}^{3} y}{\mathrm{d} x^3} + \frac{\mathrm{d} y}{\mathrm{d} x} = x$ Option 3) $\frac{\mathrm{d}^{2} y}{\mathrm{d} x^2} + \frac{\mathrm{d} y}{\mathrm{d} x} = x$ Option 4) $\frac{\mathrm{d}^{4} y}{\mathrm{d} x^4} = x$

H Himanshu

As we have learnt,

Second Order Differential Equation -

$\frac{d^{2}y}{dx^{2}}= f\left ( x \right )$

- wherein

$\frac{d^{2}y}{dx^{2}}= \sin x$

Only (C) has highest derivative two, so order will be two

Option 1)

$\frac{\mathrm{d} y}{\mathrm{d} x} = \ln x$

Option 2)

$\frac{\mathrm{d}^{3} y}{\mathrm{d} x^3} + \frac{\mathrm{d} y}{\mathrm{d} x} = x$

Option 3)

$\frac{\mathrm{d}^{2} y}{\mathrm{d} x^2} + \frac{\mathrm{d} y}{\mathrm{d} x} = x$

Option 4)

$\frac{\mathrm{d}^{4} y}{\mathrm{d} x^4} = x$

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