(Solved): 4 (3) The following differential equation describes an RC circuit where R is the resistor, C the cap ...

(3) The following differential equation describes an $$RC$$ circuit where $$R$$ is the resistor, $$C$$ the capacitor, and $$Q(t)$$ is the capacitor's charge at any time $$t$$. $$R\frac{dQ}{dt}+\frac{1}{C}Q=0$$ Let $$R=10$$ and $$C=2$$. Suppose that the initial charge on the capacitor is $$Q(0)=Q_0$$. Find the charge $$Q(t)$$ for $$t?0$$, and determine how long it takes for the charge to reach $$10\%$$ of its initial value (4) Solve the following initial value problem $$x^3{y}^{?}=y^3+x^{2}y;y(1)=5$$