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In Exercises $7-14,$ find the general solution of the first-order linear differential equation for $x>0 $$(y+1) \cos x d x-d y=0$$

In Exercises $17-24,$ find the particular solution of the first- order linear differential equationfor $x>0$ that satisfies the initial condition.

$$\begin{array}{ll}{\text { Differential Equation }} & {\text { Initial Condition }} \\ {y^{\prime}+y \tan x=\sec x+\cos x} & {y(0)=1}\end{array}$$

$$\begin{array}{ll}{\text { Differential Equation }} & {\text { Initial Condition }} \\ {y^{\prime}+\left(\frac{1}{x}\right) y=0} & {y(2)=2}\end{array}$$

$$\begin{array}{ll}{\text { Differential Equation }} & {\text { Initial Condition }} \\ {x d y=(x+y+2) d x} & {y(1)=10}\end{array}$$

In Exercises 33 and $34,$ use the differential equation for electric circuits given by $$L \frac{d I}{d t}+R I+E$$In this equation, $I$ is the current, $R$ is the resistance, $L$ is the inductance, and $E$ is the electromotive force (voltage).Solve the differential equation for the current given a constant voltage $E_{0}$.

Using an Integrating Factor The expression $u(x)$ is an integrating factor for $y^{\prime}+P(x) y=Q(x) .$ Which of the following is equal to $u^{\prime}(x) ?$ Verify your answer.(a) $P(x) u(x) \quad$ (b) $P^{\prime}(x) u(x)$(c) $Q(x) u(x) \quad$ (d) $Q^{\prime}(x) u(x)$