solvefor y,z=x^2sin(xy^2)

Solución

resolver para

y, z = x^{2} sin (x y^{2})

y = \frac{arcsin ( \frac{z}{x ^{2}} ) + 2 πn}{x}, y = - \frac{arcsin ( \frac{z}{x ^{2}} ) + 2 πn}{x}, y = \frac{π + arcsin ( - \frac{z}{x ^{2}} ) + 2 πn}{x}, y = - \frac{π + arcsin ( - \frac{z}{x ^{2}} ) + 2 πn}{x}

Pasos de solución

z = x^{2} sin (x y^{2})

Intercambiar lados

x^{2} sin (x y^{2}) = z

Dividir ambos lados entre

x^{2}; x \neq = 0

sin (x y^{2}) = \frac{z}{x ^{2}}; x \neq = 0

Aplicar propiedades trigonométricas inversas

x y^{2} = arcsin (\frac{z}{x ^{2}}) + 2 πn, x y^{2} = π + arcsin (- \frac{z}{x ^{2}}) + 2 πn

Resolver

x y^{2} = arcsin (\frac{z}{x ^{2}}) + 2 πn : y = \frac{arcsin ( \frac{z}{x ^{2}} ) + 2 πn}{x}, y = - \frac{arcsin ( \frac{z}{x ^{2}} ) + 2 πn}{x}; x \neq = 0

Resolver

x y^{2} = π + arcsin (- \frac{z}{x ^{2}}) + 2 πn : y = \frac{π + arcsin ( - \frac{z}{x ^{2}} ) + 2 πn}{x}, y = - \frac{π + arcsin ( - \frac{z}{x ^{2}} ) + 2 πn}{x}; x \neq = 0

y = \frac{arcsin ( \frac{z}{x ^{2}} ) + 2 πn}{x}, y = - \frac{arcsin ( \frac{z}{x ^{2}} ) + 2 πn}{x}, y = \frac{π + arcsin ( - \frac{z}{x ^{2}} ) + 2 πn}{x}, y = - \frac{π + arcsin ( - \frac{z}{x ^{2}} ) + 2 πn}{x}

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