Engineering Mathematics - Differential Equations

Consider differential equation $\frac{dy}{dx} + xy = x$ with the condition as y = 0 at x = 0. The value of y at x = 1.0 is ________ (rounded off to two decimal places).

The "order" of the following ordinary differential equation is ______. $d^3y/dx^3 + (d^2y/dx^2)^6 + (dy/dx)^4 + y = 0$

Pick the CORRECT solution for the following differential equation $\frac{dy}{dx} = e^{x-y}$

Consider the differential equation given below. Using the Euler method with the step size (h) of 0.5, the value of y at x = 1.0 is equal to ________ (rounded off to 1 decimal place). dy/dx = y + 2x - x²; y(0) = 1 (0 ≤ x...

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

For the equation $\frac{d^3y}{dx^3} + x (\frac{dy}{dx})^{3/2} + x^2y = 0$ the correct description is