List of top Engineering Mathematics Questions on Differential Equations asked in GATE AG

The value of \( y \) at \( x = 0.3 \) and \( y(x = 0) = 0 \) for the differential equation \[ \frac{dy}{dx} = 3y + 2e^x \] is _________. (Rounded off to 3 decimal places)

The value of \( y \) at \( x = 0.3 \) and \( y(x = 0) = 0 \) for the differential equation \[ \frac{dy}{dx} = 3y + 2e^x \] is _________. (Rounded off to 3 decimal places)

Given that \[ \frac{dy}{dx} = 2x + y, y(0) = 1 \] Using Runge-Kutta fourth order method, the value of \(y\) at \(x = 0.2\) is \underline{\hspace{2cm}} (rounded off to 3 decimal places).

\(y=ae^{mx}+be^{-mx}\) is the solution of the differential equation: