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solvefor x,(d^2-3d+2)y=sin(e^x)

Solución

resolver para

x, (d^{2} - 3 d + 2) y = sin (e^{x})

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn), x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

Pasos de solución

(d^{2} - 3 d + 2) y = sin (e^{x})

Intercambiar lados

sin (e^{x}) = (d^{2} - 3 d + 2) y

Aplicar propiedades trigonométricas inversas

sin (e^{x}) = (d^{2} - 3 d + 2) y

Soluciones generales para

sin (e^{x}) = (d^{2} - 3 d + 2) y

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn, e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn, e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

Resolver

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn : x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn

Aplicar las leyes de los exponentes

e^{x} = arcsin ((d^{2} - 3 d + 2) y) + 2 πn

f (x) = g (x)

, entonces

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

Aplicar las propiedades de los logaritmos:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn)

Resolver

e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn : x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

Aplicar las leyes de los exponentes

e^{x} = π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn

f (x) = g (x)

, entonces

ln (f (x)) = ln (g (x))

ln (e^{x}) = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

Aplicar las propiedades de los logaritmos:

ln (e^{a}) = a

ln (e^{x}) = x

x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

x = ln (arcsin ((d^{2} - 3 d + 2) y) + 2 πn), x = ln (π + arcsin (- (d^{2} - 3 d + 2) y) + 2 πn)

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tan^{2} (x) cot (x) = 1

2 sin^{2} (x) - cos^{2} (x) - 4 sin (x) + 2 = 0