second order

Which of the following equations belong/belongs to the class of second-order, linear, homogeneous partial differential equations:

Let y be the solution of the initial value problem y'' + 0.8y' + 0.16y = 0, where y(0) = 3 and y'(0) = 4.5. Then, y(1) is equal to ________ (rounded off to 1 decimal place).

The solution of the second-order differential equation $\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + y = 0$ with boundary conditions $y(0) = 1$ and $y(1) = 3$ is

Consider the following second-order differential equation: $y'' - 4y' + 3y = 2t - 3t^2$ The particular solution of the differential equation is

The solution (up to three decimal places) at x = 1 of the differential equation $\frac{d^2 y}{dx^2} + 2\frac{dy}{dx} + y = 0$ subject to boundary conditions $y(0) = 1$ and $\frac{d...

The solution $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 17y = 0;$$ $$y\left( 0 \right) = 1,{\left( {{{d\,y} \over {d\,x}}} \right)_{x = {\raise0.5ex\hbox{$\scriptstyle \pi...