Question #$2\{15$ marks$\}$

By first identifying each of the following first order Ordinary Differential Equations $($ODE$)$ as either separable, homogenous, linear or exact, solve each with the appropriate method.

a$)y^{\text{'}}cos{h}^{2}x=si{n}^{2}y,y(0)=\frac{}{2}$

$(4$ marks$)$

b$)(2xydx+dy)e^{x^2}=0,y(0)=2$

$(6$ marks$)$

c$)y^{\text{'}}+ysinx=e^{cosx},y(0)=-2\mathrm{.}5$

$(5$ marks$)$