The order and degree of the differential equation $\Big(\frac{\text{d}^3\text{y}}{\text{d}\text{x}^3}\Big)^2-3\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+2\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)^4=\text{y}^4$ are:
Solution:
Given that $\Big(\frac{\text{d}^3\text{y}}{\text{d}\text{x}^3}\Big)^2-3\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+2\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)^4=\text{y}^4$
$\therefore\text{Order}=3\text{ and degree}=2$
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$a_{i j}= 1 , \quad\quad\text { if } i=j$
$\quad\quad-x ,\quad \text { if }|i-j|=1$
$\quad\quad2 x+1, \text { otherwise }$
Let a function f: $\mathrm{R} \rightarrow \mathrm{R}$ be defined as $\mathrm{f}(\mathrm{x})=\operatorname{det}(\mathrm{A})$. Then the sum of maximum and minimum values of $f$ on $R$ is equal to:
Statement $-1 :$ $gof $ is differentiable at $x=0$ and its derivative is continuous at that point
Statement $-2 :$ $gof $ is twice differentiable at $x=0 $
$A=\left\{(x, y):|\cos x-\sin x| \leq y \leq \sin x, 0 \leq x \leq \frac{\pi}{2}\right\}$