Upcoming SlideShare
×

# Ecuación diferencial lineal

340 views
275 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
340
On SlideShare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
3
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Ecuación diferencial lineal

1. 1. Ecuación diferencial lineal.<br />Factor integrante.<br />
2. 2. Separamos / dividimos:<br />𝑑𝑦𝑑𝑥+𝑐𝑜𝑠3𝑥𝑐𝑜𝑠2𝑥 𝑠𝑒𝑛𝑥𝑦=1𝑐𝑜𝑠2𝑥 𝑠𝑒𝑛𝑥<br />y’+𝑐𝑜𝑠𝑥𝑠𝑒𝑛𝑥𝑦=1𝑐𝑜𝑠2𝑥 𝑠𝑒𝑛 𝑥𝑝𝑥=cos𝑥𝑠𝑒𝑛 𝑥 <br /> <br />𝑐𝑜𝑠2𝑥 𝑠𝑒𝑛 𝑥 𝑑𝑦𝑑𝑥+𝑐𝑜𝑠3𝑥𝑦=1<br /> <br />
3. 3. ∫𝑝𝑥=ʃcos𝑥𝑠𝑒𝑛 𝑥𝑑𝑥<br /> µ=senx<br />Multiplicamos la ecuación por el factor integrante:<br />sen x y’+ sen x 𝑐𝑜𝑠𝑥𝑠𝑒𝑛𝑥𝑦=𝑠𝑒𝑛𝑥𝑐𝑜𝑠2𝑠𝑒𝑛𝑥 <br />sen x y’+ cos x y =1𝑐𝑜𝑠2 𝑥<br /> <br />Integramos:<br />
4. 4. 𝑑(𝑠𝑒𝑛 𝑥 𝑦)𝑑𝑥=𝑠𝑒𝑐2𝑥<br />ʃ 𝑑(𝑠𝑒𝑛 𝑥 𝑦)𝑑𝑥𝑑𝑥=ʃ𝑠𝑒𝑐2𝑥 𝑑𝑥<br />y sen x = tan x + c<br />ysen x =𝑠𝑒𝑛𝑥𝑐𝑜𝑠𝑥+𝑐<br /> <br />Seguimos integrando:<br />
5. 5. y=𝑠𝑒𝑛 𝑥cos𝑥 𝑠𝑒𝑛 𝑥+𝑐𝑠𝑒𝑛 𝑥<br />y= 1cos𝑥+𝑐𝑠𝑒𝑛 𝑥<br />Finalmente encontramos:<br />y= sec x + csc x<br /> <br />Despejamos y, obtenemos el resultado.<br />