# Math Help - help to solve this differentail equation

1. ## help to solve this differentail equation

Hi Guys

i need help to solve this differentail equation :

cos^2 x sinx d' =cos^3x.y+1

i tried many times to solve this question but i could not

2. ## Re: help to solve this differentail equation

You probably haven't received any help yet because the way you have posted your DE is difficult to read.

\displaystyle \begin{align*} \cos^2{(x)} \sin{(x)} \,\frac{\mathrm{d}y}{\mathrm{d}x} = y\cos^3{(x)} + 1 \end{align*}

Yes correct

4. ## Re: help to solve this differentail equation

Rewrite it as

\displaystyle \begin{align*} \cos^2{(x)}\sin{(x)}\,\frac{\mathrm{d}y}{\mathrm{d }x} &= y\,\cos^3{(x)} + 1 \\ \frac{\mathrm{d}y}{\mathrm{d}x} &= \frac{y\,\cos^3{(x)} + 1}{\cos^2{(x)}\sin{(x)}} \\ \frac{\mathrm{d}y}{\mathrm{d}x} &= y\,\frac{\cos{(x)}}{\sin{(x)}} + \frac{1}{\cos^2{(x)}\sin{(x)}} \\ \frac{\mathrm{d}y}{\mathrm{d}x} - \frac{\cos{(x)}}{\sin{(x)}}\,y &= \frac{1}{\cos^2{(x)}\sin{(x)}} \end{align*}

This is now first order linear, so you can solve the DE using an integrating factor.

Thanks bro.