Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independent and dependent variables respectively?

Match the application to appropriate numerical method

Applications
$$P1:$$ Numerical integration
$$P2:$$ Solution to a transcendental equation
$$P3:$$ Solution to a system of linear equations
$$P4:$$ Solution to a differential equation

Numerical Method
$$M1:$$ Newton-Raphson Method
$$M2:$$ Runge-Kutta Method
$$M3:$$ Simpson's $$1/3-$$rule
$$M4:$$ Gauss Elimination Method

Consider the building block called 'Network N' shown in the figure.
Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$.

Two such blocks are connected in cascade, as shown in the figure.

The transfer function $${{{V_3}\left( s \right)} \over {{V_1}\left( s \right)}}$$ of the cascaded network is

For the Y-network shown in the figure, the value of R₁ (in Ω) in the equivalent ∆ -network is ________.