91Ó°ÊÓ

Identify each of the differential equations as to type (for example, separable, linear first order, linear second order, etc.), and then solve it. \(x^{2} y^{\prime}-x y=1 / x\)

Find the general solution of each of the following differential equations. \(y^{\prime}+y=e^{x}\)

Solve the following differential equations. \(y^{\prime}+y=x y^{2 / 3}\)

Find the "general solution" (that is, a solution containing an arbitrary constant) of each of the following differential equations, by separation of variables. Then find a particular solution of each equation satisfying the given boundary conditions. \(x y^{\prime}=y\), \(y=3\) when \(x=2\).

Solve the following differential equations. \(y^{\prime \prime}+y^{\prime}-2 y=0\)

Find the "general solution" (that is, a solution containing an arbitrary constant) of each of the following differential equations, by separation of variables. Then find a particular solution of each equation satisfying the given boundary conditions. \(x \sqrt{1-y^{2}} d x+y \sqrt{1-x^{2}} d y=0, \quad y=\frac{1}{2}\) when \(x=\frac{1}{2}\).

Find the general solution of each of the following differential equations. \(x^{2} y^{\prime}+3 x y=1\)

Solve the following differential equations. \(y^{\prime \prime}-4 y^{\prime}+4 y=0\)

Solve the following differential equations. \(y^{\prime}+\frac{1}{x} y=2 x^{3 / 2} y^{1 / 2}\)

Identify each of the differential equations as to type (for example, separable, linear first order, linear second order, etc.), and then solve it. \(x(\ln y) y^{\prime}-y \ln x=0\)