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Magazine Problem 4
Find the general solution of the differential equation. $$y^{\prime \prime}+2 y^{\prime}+6 y=0$$
Problem 4
Find the recurrence relation and general power series solution of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}.\) $$y^{\prime \prime}-x y^{\prime}-2 y=0$$
Problem 4
A series circuit has an inductor of 0.6 henry, a resistor of 400 ohms and a capacitor of \(2 \times 10^{-4}\) farad. The initial charge on the capacitor is \(10^{-6}\) coulomb and there is no initial current. Find the charge on the capacitor and the current at any time \(t\).
Problem 5
Find the general solution of the equation. $$u^{\prime \prime}+2 u^{\prime}+10 u=26 e^{-3 t}$$
Problem 5
A series circuit has an inductor of 0.5 henry, a resistor of 2 hms and a capacitor of 0.05 farad. The initial charge on the capacitor is zero and the initial current is 1 A. A voltage source of \(E(t)=3 \cos 2 t\) volts is analogous to an external force. Find the charge on the capacitor and the current at any time \(t\).
Problem 5
Find the general solution of the differential equation. $$y^{\prime \prime}-2 y^{\prime}+5 y=0$$
Problem 5
Find the recurrence relation and general power series solution of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}.\) $$y^{\prime \prime}-x y^{\prime}=0$$
Problem 6
Find the recurrence relation and general power series solution of the form \(\sum_{n=0}^{\infty} a_{n} x^{n}.\) $$y^{\prime \prime}+2 x y=0$$
Problem 6
Find the general solution of the equation. $$u^{\prime \prime}-2 u^{\prime}+5 u=10 e^{2 t}$$
Problem 6
A series circuit has an inductor of 0.2 henry, a resistor of 20 ohms and a capacitor of 0.1 farad. The initial charge on the capacitor is zero and there is no initial current. A voltage source of \(E(t)=0.4 \cos 4 t\) volts is analogous to an external force. Find the charge on the capacitor and the current at any time \(t\).
