ODE

Let $y$ be the solution of the initial value problem $y^{\prime}+0.8 y+0.16 y=0$ where $y(0)=3$ and $y^{\prime}(0)=4.5$. Then, $y(1)$ is equal to__________ (rounded off to 1 decima...

Consider two Ordinary Differential Equations (ODEs): P: $\frac{dy}{dx} = \frac{x^4+3x^2y^2+2y^4}{x^3y}$ Q: $\frac{dy}{dx} = \frac{-y^2}{x^2}$ Which one of the following options is...

In the differential equation $\frac{dy}{dx}+\alpha\ x\ y =0, \alpha$ is a positive constant. If y = 1.0 at x = 0.0, and y = 0.8 at x = 1.0, the value of α is ________ (rounded off...

For the Ordinary Differential Equation $\frac{d^2x}{dt^2} - 5\frac{dx}{dt} + 6x = 0$, with initial conditions $x(0) = 0$ and $\frac{dx}{dt}(0) = 10$, the solution is

An ordinary differential equation is given below. $\left(\frac{dy}{dx}\right) (x \ln x) = y$ The solution for the above equation is (Note: K denotes a constant in the options)

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 of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at $$x=1$$ is