CUET Preparation Today
In which of the following differential equations is the degree equal to its order? |
$x^3 \left(\frac{dy}{dx}\right) - \frac{d^3y}{dx^3} = 0$ $\left(\frac{d^3y}{dx^3}\right)^3 + \sin\left(\frac{dy}{dx}\right) = 0$ $x^2 \left(\frac{dy}{dx}\right)^4 + \sin y - \left(\frac{d^2y}{dx^2}\right)^2 = 0$ $\left(\frac{dy}{dx}\right)^3 + x \left(\frac{d^2y}{dx^2}\right) - y^3 \left(\frac{d^3y}{dx^3}\right) + y = 0$ |
$x^2 \left(\frac{dy}{dx}\right)^4 + \sin y - \left(\frac{d^2y}{dx^2}\right)^2 = 0$ |
The correct answer is Option (3) → $x^2 \left(\frac{dy}{dx}\right)^4 + \sin y - \left(\frac{d^2y}{dx^2}\right)^2 = 0$ ## The order and degree of the differential equation $x^3 \left(\frac{dy}{dx}\right) - \frac{d^3y}{dx^3} = 0$ is 3 and 1. The order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^3 + \sin\left(\frac{dy}{dx}\right) = 0$ is 3 and not defined. The degree of above differential equation is not defined because when we expand $\sin\left(\frac{dy}{dx}\right)$ we get an infinite series in the increasing powers of $\frac{dy}{dx}$. Therefore, its degree is not defined. The order and degree of the differential equation $x^2 \left(\frac{dy}{dx}\right)^4 + \sin y - \left(\frac{d^2y}{dx^2}\right)^2 = 0$ is 2 and 2. The order and degree of the differential equation $\left(\frac{dy}{dx}\right)^3 + x \left(\frac{d^2y}{dx^2}\right) - y^3 \left(\frac{d^3y}{dx^3}\right) + y = 0$ is 3 and 1. |
