Question

$( \frac{ {d}^{2} y }{d {x}^{2} } ) + \frac{dy}{dx} - 5 = 0$
Find the order and degree of the following differential equation and also state that if it is linear or non-linear​

Answer 1

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Order of a DE: Order is calculated by checking higher order derivative of x. All DE have order.

Degree of DE: Degree is the power of highest order derivative,when complete equation is free from radicals. Every differential equation does not have degree.

Here in the give DE

(\frac{d^{2}y}{dx^{2}})^{2}+(\frac{dy}{dx})^{3}=e^{x}(

dx 2 d 2 y) 2 +( dxdy ) 3 =e x

here highest derivative is :2

\begin{gathered} \frac{ {d}^{2}y }{ {dx}^{2} } \\ \end{gathered}

dx 2 d 2 y

ie Order is 2.

and the complete equation is free from radicals, thus power of double derivative ia degree of it.

Degree = 2