91Ó°ÊÓ

In problem$\mathbf{1}\mathbf{-}\mathbf{6}$ , determine whether the differential equation is separable$\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{x}}\mathbf{=}\frac{\mathbf{y}\mathbf{}{\mathbf{e}}^{\mathbf{x}\mathbf{+}\mathbf{y}}}{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{2}}$.

Question: In Problems 1-30, solve the equation.

$\text{ }\frac{\mathrm{dy}}{\mathrm{dx}}\mathbf{+}\frac{3y}{x}\mathbf{=}{\mathbf{x}}^2\mathbf{-}\mathbf{4}\mathbf{x}\mathbf{+}\mathbf{3}$

In Problems , identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x alone or y alone.

$\left({\mathbf{x}}^{\mathbf{2}}\mathbf{sinx}\mathbf{+}\mathbf{4}\mathbf{y}\right)\mathbf{dx}\mathbf{+}\mathbf{xdy}\mathbf{=}\mathbf{0}$

In problems 1-8 Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.

$\mathbf{xydx}\mathbf{+}\mathbf{dy}\mathbf{=}\mathbf{0}$

In Problems \(1 - 6\), determine whether the given equation is separable, linear, neither, or both.

\({\bf{x}}\frac{{{\bf{dx}}}}{{{\bf{dt}}}}{\bf{ + x}}{{\bf{t}}^{\bf{2}}}{\bf{ = sin}}\;{\bf{t}}\).

In problem $\mathbf{1}\mathbf{-}\mathbf{6}$, determine whether the differential equation is separablerole="math" localid="1654775979001" $\mathbf{(}\mathit{x}{\mathit{y}}^{\mathbf{2}}\mathbf{+}\mathbf{3}{\mathit{y}}^{\mathbf{2}}\mathbf{)}\mathit{d}\mathit{y}\mathbf{-}\mathbf{2}\mathit{x}\mathbf{}\mathit{d}\mathit{x}\mathbf{=}\mathbf{0}$.

Question: In Problems 1-30, solve the equation.

$\text{ }\left[\mathbf{sin}\left(\mathrm{xy}\right)\mathbf{+}\mathbf{x}\text{ }\mathbf{y}\text{ }\mathbf{cos}\left(\mathrm{xy}\right)\right]\mathbf{dx}\mathbf{+}\left[\mathbf{1}\mathbf{+}{\mathbf{x}}^2\mathbf{cos}\left(\mathrm{xy}\right)\right]\mathbf{dy}\mathbf{=}\mathbf{0}$

In Problems , identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x alone or y alone.

$\left(\mathbf{2}{\mathbf{y}}^{\mathbf{2}}\mathbf{x}\mathbf{-}\mathbf{y}\right)\mathbf{dx}\mathbf{+}\mathbf{xdy}\mathbf{=}\mathbf{0}$

In problems 1-8 Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.

${\mathbf{y}}^{\mathbf{2}}\mathbf{dx}\mathbf{+}\mathbf{(}\mathbf{2}\mathbf{xy}\mathbf{+}\mathbf{cos}\mathbf{y}\mathbf{)}\mathbf{dy}\mathbf{=}\mathbf{0}$

In Problems \(1 - 6\), determine whether the given equation is separable, linear, neither, or both.

\({\bf{3r = }}\frac{{{\bf{dr}}}}{{{\bf{d\theta }}}}{\bf{ - }}{{\bf{\theta }}^{\bf{3}}}\).