Math Help - differential equations

1. differential equations

Can anyone help me with this

cos(^2)x.(dy/dx) +y = tanx

i followed the general way but i can't integrate tanxsec^2x.e^tanx

thanks

2. Originally Posted by Dili
Can anyone help me with this

cos(^2)x.(dy/dx) +y = tanx

i followed the general way but i can't integrate tanxsec^2x.e^tanx

thanks
Let tanx=u, then integrate (ue^u)du

3. Originally Posted by Dili
i followed the general way but i can't integrate tanxsec^2x.e^tanx
Add & subtract $e^{\tan{x}}\cdot\sec^2x$

Then group some terms to turn the integrand into a product's function derivative.

The general solution to your differential equation is $\color{blue}y=k\cdot{e}^{-\tan{x}}+\tan{x}-1,~~k\in\mathbb{R}$