Question

Write the degree of the differential equation $x^{3}\left(\frac{d^{2}y}{d x^{2}}\right)^{2}+x\left(\frac{d y}{d x}\right)^{4}=0$

If matrix A = $\left(\begin{array}{l l }2 & -2 \\ -2 & 2\end{array}\right)$ and A² = pA, then write the value of p.

Find : $\textstyle\int\!{\frac{1}{x(1+\log x)}}\,d x$

L and M are two points with position vectors $2\stackrel{\rightarrow}{a}-\stackrel{\rightarrow}{b}$ and $\stackrel{\rightarrow}{a}+2\stackrel{\rightarrow}{b}$ respectively. Write the position vectors of a point N which divides the line segment LM in the ratio 2:1 externally.

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .

Write the value of $\textstyle\int\!{\frac{\ d x}{x^{2}+16}}$

If A is square matrix of order 2 and $|a d j A|=9,$ , find | A |.