Chapter 8: Ordinary Differential Equations

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.

$\left(xcosy-e^{-siny}\right)\mathit{d}\mathit{y}\mathbf{+}\mathit{d}\mathit{x}\mathbf{=}\mathbf{0}$

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.

$\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{x}\mathit{d}\mathit{y}\mathbf{+}\left[si{n}^{2}x+(x+y)sin2x\right]\mathit{d}\mathit{x}\mathbf{=}\mathbf{0}$

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.

${\mathit{x}}^{\mathbf{2}}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{-}\mathit{x}\mathit{y}\mathbf{=}\mathbf{1}\mathbf{/}\mathit{x}$

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.

${\mathit{y}}^{\mathbf{\text{'}}\mathbf{\text{'}}}\mathbf{-}\mathbf{2}{\mathit{y}}^{\mathbf{\text{'}}}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{5}\mathit{x}\mathbf{+}\mathbf{4}{\mathit{e}}^{\mathbf{x}}\mathbf{(}\mathbf{1}\mathbf{+}\mathit{s}\mathit{i}\mathit{n}\mathbf{2}\mathit{x}\mathbf{)}$

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.

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

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.

${\mathbf{(}\mathbf{D}\mathbf{-}\mathbf{2}\mathbf{)}}^{\mathbf{2}}\left(D^2+9\right)\mathit{y}\mathbf{=}\mathbf{0}$

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.

$\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }\mathit{d}\mathit{r}\mathbf{-}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{\theta }\mathit{d}\mathit{\theta }\mathbf{=}\mathit{r}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathit{\theta }\mathit{d}\mathit{\theta }$

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.

x(yy" + y'2) = yy' Hint : Let u = yy'.

Question: In Problemsto , find a particular solution satisfying the given conditions.

Question: In Problems 25to 28 , find a particular solution satisfying the given conditions.

when x = 2.