# Thread: 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

so please help me to solve question

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.

Is this your DE?

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

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

Yes correct

Please solve it

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.

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

Thanks bro.

Is this complete answer ??

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

No, now you actually have to solve the DE... Have you tried anything at all?