91Ó°ÊÓ

Find the recurrence relation and general power series solution of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}.\) $$y^{\prime \prime}+2 x y^{\prime}+4 y=0$$

Find the general solution of the equation given the particular solution. $$u^{\prime \prime}+2 u^{\prime}+5 u=15 e^{-2 t}, u_{p}(t)=3 e^{-2 t}$$

A series circuit has an inductor of 0.4 henry, a resistor of 200 ohms and a capacitor of \(10^{-4}\) farad. The initial charge on the capacitor is \(10^{-5}\) coulomb and there is no initial current. Find the charge on the capacitor and the current at any time \(t\).

Find the general solution of the differential equation. $$y^{\prime \prime}-2 y^{\prime}-8 y=0$$

Find the general solution of the equation given the particular solution. $$u^{\prime \prime}+2 u^{\prime}-8 u=14 e^{3 t}, u_{p}(t)=2 e^{3 t}$$

Find the recurrence relation and general power series solution of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}.\) $$y^{\prime \prime}+4 x y^{\prime}+8 y=0$$

Find the general solution of the differential equation. $$y^{\prime \prime}-2 y^{\prime}-6 y=0$$

Find the recurrence relation and general power series solution of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}.\) $$y^{\prime \prime}-x y^{\prime}-y=0$$

Find the general solution of the equation given the particular solution. $$u^{\prime \prime}+4 u^{\prime}+4 u=4 t^{2}, u_{p}(t)=t^{2}-2 t+\frac{3}{2}$$

Find the general solution of the differential equation. $$y^{\prime \prime}-4 y^{\prime}+4 y=0$$