Engineering Mat...

The partial differential equation \(\frac{{{\partial ^2}u}}{{\partial {t^2}}} - {c^2}\left( {\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}}} \right) = 0\); where c ≠ 0 is known as

Determine xz_x + yz_y for the function \(z = {\sin ^{ - 1}}\left( {\frac{{{x^3} + {y^3}}}{{x - y}}} \right)\)

Find the Laplace transform of y(t) = te^-5t

General solution of the Cauchy-Euler equation \({x^2}\frac{{{d^2}y}}{{d{x^2}}} - 7x\frac{{dy}}{{dx}} + 16y = 0\) is

If \(u = {\tan ^{ - 1}}\left( {\frac{{{y^3} - {x^3}}}{{{x^2} + {y^2} + xy}}} \right)\) the value of \(x\frac{{\partial u}}{{\partial x}} + y\frac{{\partial u}}{{\partial y}}\) at x = 1 and y = 3 is _____

The solution of the differential equation \(y'' + y = t,y\left( 0 \right) = 1,y'\left( 0 \right) = - 2\) is

The solution of differential equation \(\frac{{dy}}{{dx}} + \frac{y}{x} = x,\) with condition that y = 1 at x = 1, is

Find the Laplace transform of \(\mathop \smallint \limits_0^\infty \frac{{{e^{ - at}} - {e^{ - bt}}}}{t}dt\)

What is the value of y(1) if y(0) = 4 and y’(0) = 9 for the differential equation y’’ + 4y’ + 4y = e^2x

The complementary solution of the differential equation \({x^2}\frac{{{d^3}y}}{{d{x^3}}} - 4x\frac{{{d^2}y}}{{d{x^2}}} + 6\frac{{dy}}{{dx}} = 4\) is