Engineering Mat...

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

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

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

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

The differential equation is, y’ + y tan x = cos x, y(0) = 0.

The solution of a differential equation \(\frac{{dy}}{{dt}} - y = {e^{3t}}\) with an initial condition y(0) = 2 is Ae^t + Be^3t. The value of A + B is ______

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

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

Solution of the differential equation \(20{y}''+4{y}'+y=0\) with initial conditions y(0) = 3.2 and \({y}'\left( 0 \right)=0\) is

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