91影视

Use the method discussed under 鈥淗omogeneous Equations鈥� to solve problems 9-16.

$\mathbf{(}\mathbf{3}{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{y}}^{\mathbf{2}}\mathbf{)}\mathbf{dx}\mathbf{}\mathbf{+}\mathbf{}\mathbf{(}\mathbf{xy}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{x}}^{\mathbf{3}}{\mathbf{y}}^{\mathbf{-}\mathbf{1}}\mathbf{)}\mathbf{dy}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$

In Problems 9鈥�20, determine whether the equation is exact.

If it is, then solve it.

$\mathbf{(}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{)}\mathbf{dx}\mathbf{+}\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{y}\mathbf{)}\mathbf{dy}\mathbf{=}\mathbf{0}$

In Problems 7-12, solve the equation.

$鈥�\left(\mathbf{2}{\mathbf{y}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{y}\mathbf{+}\mathbf{4}{\mathbf{x}}^{\mathbf{2}}\right)\mathbf{dx}\mathbf{+}\left(\mathbf{2}\mathbf{xy}\mathbf{+}\mathbf{x}\right)\mathbf{dy}\mathbf{=}\mathbf{0}$

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

$\text{鈥�}\left[\mathbf{1}\mathbf{+}{\left(\mathbf{1}\mathbf{+}{\mathbf{x}}^2\mathbf{+}\mathbf{2}\mathbf{xy}\mathbf{+}{\mathbf{y}}^2\right)}^{-1}\right]\mathbf{dx}\mathbf{+}\left[{\mathbf{y}}^{\mathbf{-}\frac{1}{2}}{\left(\mathbf{1}\mathbf{+}{\mathbf{x}}^2\mathbf{+}\mathbf{2}\mathbf{xy}\mathbf{+}{\mathbf{y}}^2\right)}^{-1}\right]\mathbf{dy}\mathbf{=}\mathbf{0}$

Use the method discussed under 鈥淗omogeneous Equations鈥� to solve problems 9-16.

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

In Problems 9鈥�20, determine whether the equation is exact.

If it is, then solve it.

$\mathbf{(}{\mathbf{e}}^{\mathbf{x}}\mathbf{sin}\mathbf{y}\mathbf{-}\mathbf{3}{\mathbf{x}}^{\mathbf{2}}\mathbf{)}\mathbf{dx}\mathbf{+}\left({\mathbf{e}}^{\mathbf{x}}\mathbf{cos}\mathbf{y}\mathbf{+}\frac{{\mathbf{y}}^{\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}}}{\mathbf{3}}\right)\mathbf{dy}\mathbf{=}\mathbf{0}$

In Problems 7-12, solve the equation.

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

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

$\text{鈥�}\frac{\mathrm{dx}}{\mathrm{dt}}\mathbf{=}\mathbf{1}\mathbf{+}{\mathbf{cos}}^2\left(t-x\right)$

Use the method discussed under 鈥淗omogeneous Equations鈥� to solve problems 9-16.$\left(x^2+y^2\right)\mathbf{dx}\mathbf{+}\mathbf{2}\mathbf{xy}\mathbf{}\mathbf{dy}\mathbf{=}\mathbf{0}$

In Problems 7-12, solve the equation.

$\left(\mathbf{2}{\mathbf{xy}}^{\mathbf{3}}\mathbf{+}\mathbf{1}\right)\mathbf{dx}\mathbf{+}\left(\mathbf{3}{\mathbf{x}}^{\mathbf{2}}{\mathbf{y}}^{\mathbf{2}}\mathbf{-}{\mathbf{y}}^{\mathbf{-}\mathbf{1}}\right)\mathbf{dy}\mathbf{=}\mathbf{0}$