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 $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].

If f : R→ R defined by f(x) = $\textstyle{\frac{3x+5}{2}}$ is an invertible function, then find $f^{-1}(x).$

Write the position vector of the point which divides the join of points with position vectors $3\stackrel{\rightarrow}{a}-2\stackrel{\rightarrow}{b}$ and $2\stackrel{\rightarrow}{a}+3\stackrel{\rightarrow}{b}$ in the ratio 2:1.

Find the solution of the differential equation ${\frac{d y}{d x}}=x^{3}e^{-2y}$.

If $(2x\ \ 4){\binom{x}{-8}}=0,$ find the positive value of x.