Question

Determine the order and degree of the given differential equation: $(y''')^{2}+2(y'')^{2}+3(y')+4y=0$

Answer 1

Solution:
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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

$(y''')^{2}+2(y'')^{2}+3(y')+4y=0$

here highest derivative is :3

$(y''')^{2}$

As we know that $(y''') = \frac{d^{3}y}{dx^{3}}$

ie Order is 3.

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

So, Degree = 2