Matemática

Ecuaciones Diferenciales Ejercicios De Primer Orden
ECUACIONES DIFERENCIALES

PRESENTADO POR
CRISTIAN RAMIREZ OLARTE
CARLOS BOVEA ISAZA

CORPORACIONUNIVERSITARIA DE LA COSTA
CUC
IV SEMESTRE DE INGENIERIA INDUSTRIAL
GRUPO AN
BARRANQUILLA - ATLANTICO

dy/dx=5y

dy/dx-5y=0

P_((x))=-5

e^∫▒〖-5dx〗=e^(-5x) → d/dx[e^(-5x).y]=e^(-5x) (0)

d/dx e^(-5x) y=0

e^(-5x) y=C

y=Ce^5x

dy/dx+2y=0
P_((x))=2
e^(∫2dx)=e^2x → d/dx [e^2x y]=e^2x (0)e^2x y=C
y=Ce^(-2x)

dy/dx+y=e^3x

P_((x) )=1

e^(∫dx)=e^x

d/dx [e^x y]=e^3x e^x→de^x y=e^4x dx

e^x y=1/4 e^4x+C

y=1/4 e^3x+Ce^(-x)
3dy/dx+12y=4

dy/dx+4y=4/3

P_((x) )=4

e^(∫4dx)=e^4x

d/dx [e^4x y]=4/3 e^4x

e^4x y=1/3 e^4x+C

y=Ce^(-4x)+1/3

y^'+3x^2 y=x^2

dy/dx+3x^2y=x^2

P_((x))=3x^2
e^(∫3x^2 dx)=e^(3^(x^3/3) )=e^(x^3 )
d/dx [e^(x^3 ).y]=x^2 e^(x^3 )
d[e^(x^3 ) y]=x^2 e^(x^3 ) dx
u=x^3du=3x^2dx
e^(x^3 ) y=1/3 e^(x^3 )+C
y=e^(x^3 )/(3e^(x^3 ) )+Ce^(-x^3 )
y=Ce^(-x^3 )+1/3

y^'+ 2xy= x^3

dy/dx+2xy= x^3P(x)=2x

e^∫▒2xdx=e^(2∫▒xdx)=e^(x^2 )

d/dx= (ye^(x^2 ) ) = x^3 e^(x^2 )

ye^(x^2 )= ∫▒〖x^3 e^(x^2 ) dx= 〗 ∫▒〖x^2 e^(x^2 ) x dx 〗

u=x^2 ; du=2xdxdv=e^(x^2 ) x dx ; v=1/2 e^(x^2 )

ye^(x^2 )= (x^2 e^(x^2 ))/2-1/2 ∫▒〖e^(x^2 ) 2x dx〗

ye^(x^2 )= (x^2 e^(x^2 ))/2-1/2 e^(x^2 )+ C

y=x^2/2-1/2+Ce^(-x^2 )x^2 y^'+xy=1

dy/dx+1/x y=1/x+1/x^2

P(x)=1/x 〖==>e〗^(∫▒dx/x )=e^lnx=x

d/dx [xy]=1/x x .1/x^2 x==>d[xy]=dx/x

xy=1+lnx+C

y=(1+lnx+C)/x
y^'=2y+ x^2+ 5