Chapter 8: Ordinary Differential Equations

Find the inverse transforms of the functions$F\left(p\right)$.$\frac{3p+10}{p^2-25}$

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection. Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form.

$\mathbf{(}{\mathbf{D}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\mathbf{D}\mathbf{+}\mathbf{12}\mathbf{)}\mathit{y}\mathbf{=}\mathbf{80}\mathit{s}\mathit{i}\mathit{n}\mathbf{2}\mathit{x}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

$\mathit{u}\mathbf{(}\mathbf{1}\mathbf{-}\mathit{v}\mathbf{)}\mathit{d}\mathit{v}\mathbf{+}{\mathit{v}}^{\mathbf{2}}\mathbf{(}\mathbf{1}\mathbf{-}\mathit{u}\mathbf{)}\mathit{d}\mathit{u}\mathbf{=}\mathbf{0}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

$\mathbf{(}\mathit{y}\mathbf{+}\mathbf{2}\mathit{x}\mathbf{)}\mathit{d}\mathit{x}\mathbf{-}\mathit{x}\mathit{d}\mathit{y}\mathbf{=}\mathbf{0}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

$\mathit{x}{\mathit{y}}^{\mathbf{\text{'}}\mathbf{\text{'}}}\mathbf{+}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{=}\mathbf{4}\mathit{x}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

${\mathit{y}}^{\mathbf{\text{'}}\mathbf{\text{'}}}\mathbf{+}\mathbf{4}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{26}{\mathit{e}}^{\mathbf{3}\mathbf{x}}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

${\mathit{y}}^{\mathbf{\text{'}}\mathbf{\text{'}}}\mathbf{+}\mathbf{4}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{2}{\mathit{e}}^{\mathbf{-}\mathbf{2}\mathbf{x}}\mathit{c}\mathit{o}\mathit{s}\mathit{x}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

${\mathit{y}}^{\mathbf{\text{'}}\mathbf{\text{'}}}\mathbf{-}\mathbf{4}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{+}\mathbf{4}\mathit{y}\mathbf{=}\mathbf{6}{\mathit{e}}^{\mathbf{2}\mathbf{x}}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

${\mathit{y}}^{\mathbf{\text{'}}\mathbf{\text{'}}}\mathbf{-}\mathbf{5}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{+}\mathbf{6}\mathit{y}\mathbf{=}{\mathit{e}}^{\mathbf{2}\mathbf{x}}$

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

$\mathbf{(}\mathbf{2}\mathit{x}\mathbf{+}\mathit{y}\mathbf{)}\mathit{d}\mathit{y}\mathbf{-}\mathbf{(}\mathit{x}\mathbf{-}\mathbf{2}\mathit{y}\mathbf{)}\mathit{d}\mathit{x}\mathbf{=}\mathbf{0}$