Question

Persamaan difrensial linear

1. (2x) (dy/dx) -2y = 3x lnx

Answer 1

Dy/dx +Py = Q

(2x)(dy/dx) - 2y = 3x lnx
bagi dengan 2x

dy/dx - y/x = (3/2) lnx

Faktor integrasi :

= e^(∫-(1/x) dx)
= e^(-∫(1/x) dx)
= e^(-lnx)
= 1/x , x > 0

y * faktor integrasi = ∫Q*faktor integrasi dx
y/x = ∫(3/2)lnx * (1/x) dx
y/x = 3/2∫lnx/x dx
y/x = 3/2∫lnx/x d(lnx)/(1/x)
y/x = 3/2∫lnx d(lnx)
y/x = (3/4)ln²x + c
y = x(3/4)ln²x + cx

CMIIW