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Beliebt Rechnen >

y^'=1-2cos(y)

Lösung

y^{^{'}} = 1 - 2 cos (y)

Lösung

y = 2 arctan \frac{e ^{3 c_{1}} + e ^{3 t}}{3 ( - e ^{3 c_{1}} + e ^{3 t} )} + 2 πn

Schritte zur Lösung

y^{'} (t) = 1 - 2 cos (y)

Löse nach

t, y^{'} (t) = \frac{d y}{d t} = \frac{1}{\frac{d t}{d y}} = \frac{1}{t ^{^{'}}}

(\frac{1}{t ^{^{^{'}}}}) = 1 - 2 cos (y)

Isoliere

t^{^{'}} : t^{^{'}} = \frac{1}{1 - 2 cos ( y )}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

t = \int \frac{1}{1 - 2 cos ( y )} d y

\int \frac{1}{1 - 2 cos ( y )} d y = - \frac{1}{3} (ln (3 tan (\frac{y}{2}) + 1) - ln (3 tan (\frac{y}{2}) - 1)) + c_{1}

t = - \frac{1}{3} (ln (3 tan (\frac{y}{2}) + 1) - ln (3 tan (\frac{y}{2}) - 1)) + c_{1}

Isoliere

y : y = 2 arctan \frac{e ^{3 c_{1}} + e ^{3 t}}{3 ( - e ^{3 c_{1}} + e ^{3 t} )} + 2 πn

y = 2 arctan \frac{e ^{3 c_{1}} + e ^{3 t}}{3 ( - e ^{3 c_{1}} + e ^{3 t} )} + 2 πn

Graph

Beliebte Beispiele

(dy)/(dx)=-ysin(x)

\frac{d y}{d x} = - y sin (x)

(dy)/(dx)=2y(1-y/5)

\frac{d y}{d x} = 2 y (1 - \frac{y}{5})

xe^{x^2}+yy^'=0

x e^{x^{2}} + y y^{^{'}} = 0

y^{^{'}} = e^{y} sin (x)

\frac{d x}{d y} = \frac{y}{x}