Question

Find the particular solution of the following differential equation : ${\frac{d y}{d x}}\;=1+x^{2}+y^{2}+x^{2}y^{2},$ given that y = 1, when x = 0.

If A = $\left(\begin{array}{l l }2 & 3 \\ 1 & -4\end{array}\right)$ , B = $\left(\begin{array}{l l }1 & -2 \\ -1 & 3\end{array}\right)$ , verify that $(A B)^{-1}=B^{-1}A^{-1}$

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?

A bag contains (2n + 1) coins. It is known that (n – 1) of these coins have a head on both sides, whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is 31/42, determine the value of n.

The total expenditure (in ₹) required for providing the cheap edition of a book for poor and deserving students is given by R(x) = 3x² + 36x, where x is the number of set of books. If the marginal expenditure is defined as ${\frac{d R}{d x}},$ write the marginal expenditure required for 1200 such sets.

Solve the following differential equation. (1 + y²) (1 + log |x|) dx + x dy = 0

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