tarea 3
DESCRIPTION
ecuaciones diferencialesTRANSCRIPT
![Page 1: tarea 3](https://reader036.vdocuments.pub/reader036/viewer/2022082613/563dbab9550346aa9aa7885a/html5/thumbnails/1.jpg)
Ecuaciones diferenciales
Resolución de una ecuación diferencial lineal de orden n no homogénea.
Método de variación de parámetros.
B .− y2+5 y '+6 y=1x
1.- (D2+5D+6 ) y=0
λ2+5 λ+6=0
( λ+2 ) ( λ+3 )=0
λ1=−2 , λ2=−3
yc=C1 e−2 x+C2 e
−3x
y1 ( x )=e−2 x, y2 (x)=e
−3 x
2.-y p (x)=V 1 (x)e−2x+V 2(x)e
−3 x
| e−2 x e−3x
−2e−2x −3e−3x| |V 1' (x )V 2' (x )|=|01x|
|A|=| e−2 x e−3x
−2e−2 x −3e−3x|=−3e−5x+2e−5x=e−5 x
|A1|=|0 e−3x
1x
−3e−3x|=−e−3x
x
|A2|=| e−2 x
0
−2e−2x 1x|= e−2xx
V 1' (x )= −1
xe−3 x, V 2
' (x )= −1xe−3 x
V 1' ( x )∫ −1
xe−3 x dx=−∫ e3x
x=−( ln x+3x )=−lnx−3 x
![Page 2: tarea 3](https://reader036.vdocuments.pub/reader036/viewer/2022082613/563dbab9550346aa9aa7885a/html5/thumbnails/2.jpg)
V 2' ( x )∫ −1
xe−3 x dx=−∫ e3x
x=−( ln x+3x )=−lnx−3 x
y x=(−lnx−3 x ) e−2ex+(−lnx−3 x)e−3ex
CRUZ APOLINAR DANIEL ADOLFO