Question

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

If the function f : R → R defined by f(x) = 3x - 4 is invertible, then find $f^{-1}.$

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

What is the range of the function f(x) = $\textstyle{\frac{|x-1|}{x-1}}$, x ≠ 1?

Write the element $a_{23}$ of a 3 × 3 matrix A = ($a_{i j}$) whose elements $a_{i j}$ are given by $a_{i j}=\frac{|i-j|}{2}$

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

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