Find the general solution of the differential equations: `cos^2x(dy/dx)+y= tanx ` , `(0 le x lepi/2)`

Explanation

Given,

`=>(cos^2xdy)/(dx)​+y=tanx`

`⇒(dy)/(dx)​+ysec^2x=tanxsec^2x ....(1)`

Thus,`I.F.=e^(tanx)`

Multiplying (1) by I.F,

`=>(e^(tanx)dy)/dx+e^(tanx)ysec^2x=e^(tanx)tanxsec^2x`

Integrating ,

`=>ye^(tanx)=∫e^(tanx).tanxsec^2xdx`

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