The directional derivative of the function $$f(x, y, z) = x + y$$ at the point $$P(1,1,0)$$ along the direction $$\overrightarrow i + \overrightarrow j $$ is

Solve $${{{d^4}v} \over {d{x^4}}} + 4{\lambda ^4}v = 1 + x + {x^2}$$

Using Laplace transform, solve the initial value problem $$9{y^{11}} - 6{y^1} + y = 0$$
$$y\left( 0 \right) = 3$$ and $${y^1}\left( 0 \right) = 1,$$ where prime denotes derivative with respect to $$t.$$

Shear stress in the Newtonian fluid is proportional to