The second-order differential equation in an unknown function $$u : u(x, y)$$ is defined as $$\frac{\partial^2 u}{\partial x^2}= 2$$
Assuming $$g : g(x)$$, $$f : f(y)$$, and $$h : h(y)$$, the general solution of the above differential equation is
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the student will pass in at least one of these two subjects is
For the following partial differential equation,
$x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$
which of the following option(s) is/are CORRECT?
Consider the data of $f(x)$ given in the table.
| $i$ | $0$ | $1$ | $2$ |
|---|---|---|---|
| $x_i$ | $1$ | $2$ | $3$ |
| $f(x_i)$ | $0$ | $0.3010$ | $0.4771$ |
The value of $f(1.5)$ estimated using second-order Newton’s interpolation formula is ________________ (rounded off to 2 decimal places).