Differential Equations

Consider the second-order differential equation $\frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$ with initial conditions $y(0) = 1$, $\frac{dy}{dx}|_{x=0} = 1$ The solution is given by

Which of the following differential equations is/are nonlinear?

Which of the following differential equations is/are nonlinear?

In the following differential equation, the numerically obtained value of y(t), at t =1, is ________ (Round off to 2 decimal places). $\frac{dy}{dt} = \frac{e^{-at}}{2 + at}$, α =...

Consider a system governed by the following equations $\frac{dx_1(t)}{dt} = x_2(t) - x_1(t)$ $\frac{dx_2(t)}{dt} = x_1(t) - x_2(t)$ The initial conditions are such that $x_1(0) < x...

Consider the differential equation $$\left( {{t^2} - 81} \right){{dy} \over {dt}} + 5ty = \sin \left( t \right)\,\,$$ with $$y\left( 1 \right) = 2\pi .$$ There exists a unique solu...