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The order and degree of the differential equation $3 x^2 \frac{d^2 y}{d x^2}-\sin \left(\frac{d^3 y}{d x^3}\right)+\cos (x y)=0$ are
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Order is 3 and degree can't be defined
$\because 3 x^2 \cdot \frac{d^2 y}{d x^2}-\sin \left(\frac{d^3 y}{d x^3}\right)+\cos (x y)=0$
$\Rightarrow 3 x^2 \frac{d^2 y}{d x^2}-\left[\frac{d^3 y}{d x^3}-\frac{1}{3 !}\left(\frac{d^3 y}{d x^3}\right)^3+\frac{1}{5 !}\left(\frac{d^3 y}{d x^3}\right)^5 \ldots\right]+\cos (x y)=0$
So, the order of the above differntial equation is 3 . But degree is undefined.
$\Rightarrow 3 x^2 \frac{d^2 y}{d x^2}-\left[\frac{d^3 y}{d x^3}-\frac{1}{3 !}\left(\frac{d^3 y}{d x^3}\right)^3+\frac{1}{5 !}\left(\frac{d^3 y}{d x^3}\right)^5 \ldots\right]+\cos (x y)=0$
So, the order of the above differntial equation is 3 . But degree is undefined.
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