ordinary-differential-equations

In order to numerically solve the ordinary differential equation dy/dt = -y for t > 0 , with an initial condition y(0) = 1 , the following scheme is employed: $\frac{y_{n+1} - y_{n...

The initial value problem $\rm \frac{dy}{dt}+2y=0, y(0)=1$ is solved numerically using the forward Euler’s method with a constant and positive time step of Δt. Let 𝑦 𝑛 represent...

For the exact differential equation, $\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$ which one of the following is the solution?

The differential equation $$\,{{{d^2}y} \over {d{x^2}}} + 16y = 0$$ for $$y(x)$$ with the two boundary conditions $${\left. {{{dy} \over {dx}}} \right|_{x = 0}} = 1$$ and $${\left....

Consider an ordinary differential equation $${{dx} \over {dt}} = 4t + 4.\,\,$$ If $$x = {x_0}$$ at $$t=0,$$ the increment in $$x$$ calculated using Runge-Kutta fourth order multi-s...