Solve the differential equation $${{{d^2}y} \over {d{x^2}}} + y = x\,\,$$ with the following conditions $$(i)$$ at $$x=0, y=1$$ $$(ii)$$ at $$x=0, $$ $${y^1} = 1$$

An 8085 microprocessor based system uses a 4K × 8-bit RAM whose starting address is AA00H. The address of the last byte in this RAM is

The circuit shown in Fig. is operating in steady-state with switch $${S_1}$$ closed. The switch $${S_1}$$ is opened at $$t\, = \,0$$.

(a) Find $${i_L}\left( {{0^ + }} \right)$$.
(b) Find $${e_1}\left( {{0^ + }} \right)$$.
(c) Using nodal equations and Laplace transform approach, find an expression for the voltage across the capacitor for all $$t\, = \,0$$.

When the angular frequency $$\omega $$ in Fig. is varied from $$0$$ to $$\infty $$ the locus of the current phasor $${{\rm I}_2}$$ is given by