Question

Solve the following differential equation : $x{\frac{d y}{d x}}\ +y-x+x y\cot x=0,x\neq0$

For the curve y = 4x³ – 2x⁵, find all those points at which the tangent passes through the origin.

Find the particular solution of the differential equation $e^{x}{\sqrt{1-y^{2}}}d x+\left({\frac{y}{x}}\right)d x=0$ given that y = 1 when x = 0.

Find the equation of tangent to the curve $y={\frac{x-7}{x^{2}-5x+6}}$ at the point, where it cuts the x-axis.

A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact ? Do you think that statement of B is always true ?

Find : $\textstyle\int$${\frac{x^{2}}{x^{4}+x^{2}-2}}d x$

Solve the differential equation ${\frac{d y}{d x}}\ +\ y\ \cot\ x$= 2 cos x, given that y = 0 when $x={\frac{\pi}{3}}\,.$