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  • Determine order and degree (if defined) of differential equation. d^2 y/dx^2 = cos3x + sin3x

5. Determine order and degree (if defined) of differential equation.

   \frac{d^2y}{dx^2} = \cos 3x + \sin 3x

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Given function is
\frac{d^2y}{dx^2} = \cos 3x + \sin 3x
\Rightarrow \frac{d^2y}{dx^2}- \cos 3x - \sin 3x = 0
Now, it is clear from the above that, the highest order derivative present in differential equation is  y^{''}\left ( \frac{d^2y}{dx^2} \right )

Therefore, order of given differential equation  \frac{d^2y}{dx^2}- \cos 3x - \sin 3x = 0 is  2
Now, the given differential equation is  a polynomial equation in it's derivatives  \frac{d^2y}{dx^2} and power raised to  \frac{d^2y}{dx^2} is 1
Therefore, it's  degree is 1

Posted by

Gautam harsolia

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