Question

Write the sum of the order and degree of the differential equation. $\begin{array}{r l}{\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}+\left({\frac{d y}{d x}}\right)^{3}+x^{4}\,}&{{}=0.}\end{array}$

If A = $\left(\begin{array}{l l }x & x-y \\ 2x+y & 7\end{array}\right)$ = $\left(\begin{array}{l l }3 & 1 \\ 8 & 7\end{array}\right)$ , then find the value of y.

Write the projection of the vector $7\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -4\stackrel{\wedge}{k}$ on the vector $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$.

If $\begin{vmatrix} 2x & x+3 \\ 2(x+1) & x+1 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}$, write the value of x.

If A' = $\left(\begin{array}{l l }3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l l }-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right)$ then find A' – B'.

Let R={(a,a³): a is a prime number less than 5} be a relation. Find the range of R.

Write the projection of the vector $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ along the vector $\stackrel{\rightarrow}{j}\$.