Recent activity in Electrical Engineering Mathematics

Solve the following using Taylor’s Series Method (up to 3 terms): \[ \frac{dy}{dx} = x^2 + y, \quad y(0) = 1 \] Find \( y(0.2) \).

Explain the method of separation of variables with an example.

Solve the linear homogeneous equation \[ D^2y - 5Dy + 6y = 0 \]

Solve the first-order PDE using Lagrange’s method \[ p + q = x + y \] where \( p = \frac{\partial z}{\partial x} \) and \( q = \frac{\partial z}{\partial y} \).

What is a Partial Differential Equation (PDE)? Explain with an example.