$7\mathrm{.}7$ In the circuit shown, switch $1$ has been closed and switch $2$ has been open for a long time. At $t=0,$ switch $1$ is opened. Then $10$ ms later, switch $2$ is closed. Find

a$)v_c(t)$ for $0t0\mathrm{.}01s,$

b$)v_c(t)$ for $t0\mathrm{.}01s,$

c$)$ the total energy dissipated in the $25k$ resistor, and

d$)$ the total energy dissipated in the $100k$ resistor.