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.

---

(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.

---

(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.