Question

Find the particular solution of the differential equation satisfying the given condition ${\frac{d y}{d x}}=y\tan x,$ given that y = 1, when x = 0.

The amount of pollution content added in air in a city due to x-diesel vehicles is given by p(x) = 0·005x³ + 0·02x² + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added.

Find the particular solution of the following differential equation : $(x\ +1){\frac{d y}{d x}}=2e^{-y}-1;$ y = 0 when x = 0.

Find the particular solution of the differential equation : ${\frac{d y}{d x}}\ +y\cot x=2x+x^{2}\cot x,$ x ≠ 0. Given that y = 0, when $x={\frac{\pi}{2}}\ .$

To promote the making of toilets for women, as organisation tried to generate awareness through (i) house calls (ii) letters and (iii) announcements. The cost for each mode per attempt is given below : (i) ₹ 50 (ii) ₹ 20 (iii) ₹ 40 The number of attempts made in three villages X, Y and Z and given below :

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.

P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree in stating the same fact ?