Ecuación diferencial
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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 = −dy yLn( y) Ln(x) dx + dy yLn( y) = 0 ∫ Ln(x) dx + ∫ dy yLn( y) = C u= Ln(x) du= dx x dv = dx v = x t = Ln(y) dt = dy y xLn(x) - x ∫ dx x + ∫ dt t xLn(x) – x 2 +Ln(t) =C xLn(x) - x 2 + Ln(Ln(x)) = 0
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Ecuación diferencial
Transcript of Ecuación diferencial
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
