Question

For each of the differential equations given below, indicates its order and degree (if defined).

\((i) \frac {d^2y}{dx^2}+5x(\frac {dy}{dx})^2-6y=log\ x\)

\((ii)(\frac {dy}{dx})^3-4(\frac{dy}{dx})^2+7y=sin\ x\)

\((iii) \frac {d^4y}{dx^4}-sin(\frac {d^3y}{dx^3})=0\)

Answer 1

(i) The differential equation is given as:

\(\frac {d^2y}{dx^2}+5x(\frac {dy}{dx})^2-6y=log\ x\)

⇒\(\frac {d^2y}{dx^2}+5x(\frac {dy}{dx})^2-6y-log\ x=0\)

The highest order derivative present in the differential equation is \(\frac {d^2y}{dx^2}\).Thus, its order is two.The highest power raised to \(\frac {d^2y}{dx^2}\) is one. Hence, its degree is one.

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(ii) The differential equation is given as:

\((\frac {dy}{dx})^3-4(\frac{dy}{dx})^2+7y=sin\ x\)

⇒\((ii)(\frac {dy}{dx})^3-4(\frac{dy}{dx})^2+7y-sin\ x=0\)

The highest order derivative present in the differential equation is dy/dx. Thus, its order is one.The highest power raised to \(\frac {dy}{dx}\) is three.Hence, its degree is three.

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(iii) The differential equation is given as:

\(\frac {d^4y}{dx^4}-sin(\frac {d^3y}{dx^3})=0\)

The highest order derivative present in the differential equation is \(\frac {d^4y}{dx^4}\). Thus, its order is four. However, the given differential equation is not a polynomial equation. Hence, its degree is not defined.