Engineering Mat...

If \(\frac{{{d^2}y}}{{d{t^2}}} + y = 0\) under the conditions y = 1, \(\frac{{dy}}{{dt}} = 0\), when t = 0, then y(π/2) is equal to

Which of the following equations represents a one-dimensional wave equation?

Find the values of y(1) by solving the differential equation \(y\frac{{dy}}{{dx}} = 6{x^2} + 5,\;y\left( 0 \right) = 2\)

The solution of the partial differential equation \(\frac{{{\partial ^2}z}}{{\partial {y^2}}} + z = 0\) is when \(y = 0,z = {e^x}\;and\frac{{\partial z}}{{\partial y}} = {e^{ - x}}\)

A third order ordinary differential equation with x, x ln x and x ln²x as linearly independent solutions is given by

Consider the equation \(\frac{{dy}}{{dx}} = \frac{{{y^2}}}{x}\) with the boundary y(1) = 1. Which one of the following is the correct range of x for which y is real and finite?

Particular integral of \(\left( {{x^2}{D^2} - 2} \right)y = {x^2} + \frac{1}{x}\)

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

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

The solution of a partial differential equation is in the form of z = f₁ (y - ax) + x f₂ (y - bx).

\(4\frac{{{\partial ^2}z}}{{\partial {x^2}}} + 12\frac{{{\partial ^2}z}}{{\partial x\;\partial y}} + 9\frac{{{\partial ^2}z}}{{\partial {y^2}}} = 0\)