Ecuación Diferencial Ordinaria de Variable Separable

M(x) dx + N(y) dy = 0

∫ M(x) dx + ∫ N(y) dy = C

yLn(x)Ln(y) dx + dy = 0

yLn(x)Ln(y) dx = -dy

Ln(x) dx = −dyyLn( y )

Ln(x) dx + dy

yLn( y ) = 0

∫ Ln(x) dx + ∫ dy

yLn( y ) = C

u= Ln(x) du=dxx dv = dx v = x

t = Ln(y) dt = dyy

xLn(x) - ∫xdxx + ∫

dtt

xLn(x) – x2 +Ln(t) =C

xLn(x) - x2 + Ln(Ln(x)) = 0

y dydx – sen(x)℮x+2y =0

y dy = sen(x)℮x℮2y dx

y℮-2y dy = sen(x)℮x dx

u = y du = dy ; dv = ℮-2y v = -12℮-2y

m= ℮x dm = ℮x dx ; dn = sen(x)dx n= -cos(x)

-y12℮-2y - ∫-

12℮-2y dy = -cos(x) ℮x - ∫-cos(x) ℮x dx

-y12℮-2y - ∫-

12℮-2y dy = sen(x) ℮x – cos(x) ℮x - ∫sen(x) ℮x dx

-y12℮-2y -

14 ℮-2y =

12 ℮x (sen(x) – cos(x)) + C

2y +1 = 2℮2y+x +C