91Ó°ÊÓ

A series circuit consists of a device where \(L=1 \mathrm{H}, R=20 \Omega, C=0.002 \mathrm{~F}\), and \(E(t)=12 \mathrm{~V}\). If the initial charge and current are both zero, find the charge and current at time t.

Find the general solution to the linear differential equation. $$ 8 y^{\prime \prime}+14 y^{\prime}-15 y=0 $$

Classify the differential equation. Determine the order, whether it is linear and, if linear, whether the differential equation is homogeneous or nonhomogeneous. If the equation is second-order homogeneous and linear, find the characteristic equation.\(\left(\frac{d y}{d t}\right)^{2}+y y^{\prime}=1\)

Solve the differential equation using either the method of undetermined coefficients or the variation of parameters. $$ y^{\prime \prime}+2 y^{\prime}=e^{3 x} $$

A series circuit consists of a device where \(L=\frac{1}{2} \mathrm{H}, R=10 \Omega, C=\frac{1}{50} \mathrm{~F}\), and \(E(t)=250 \mathrm{~V}\). If the initial charge on the capacitor is \(0 \mathrm{C}\) and the initial current is \(18 \mathrm{~A}\), find the charge and current at time \(t\)

Solve the differential equation using either the method of undetermined coefficients or the variation of parameters. $$ y^{\prime \prime}+6 y^{\prime}+9 y=e^{-z} $$

Find the general solution to the linear differential equation. $$ y^{\prime \prime}+81 y=0 $$

Classify the differential equation. Determine the order, whether it is linear and, if linear, whether the differential equation is homogeneous or nonhomogeneous. If the equation is second-order homogeneous and linear, find the characteristic equation.\(\frac{d^{2} y}{d t^{2}}+t \frac{d y}{d t}+\sin ^{2}(t) y=e^{t}\)

Solve the differential equation using either the method of undetermined coefficients or the variation of parameters. $$ y^{\prime \prime}+2 y^{\prime}-8 y=6 e^{2 x} $$

Find the general solution to the linear differential equation. $$ y^{\prime \prime}-y^{\prime}+11 y=0 $$