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Beliebt Rechnen >

(dx)/(dt)=sin(2pi(t+3)),x(3)=1

Lösung

\frac{d x}{d t} = sin (2 π (t + 3)), x (3) = 1

Lösung

x = - \frac{1}{2 π} cos (2 π (t + 3)) + 1 + \frac{1}{2 π}

Schritte zur Lösung

\frac{d x}{d t} = sin (2 π (t + 3))

Ersetze

\frac{d x}{d t}

mit

x^{'} (t)

x^{^{'}} (t) = sin (2 π (t + 3))

Wenn

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

dann

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

x = \int sin (2 π (t + 3)) d t

\int sin (2 π (t + 3)) d t = - \frac{1}{2 π} cos (2 π (t + 3)) + c_{1}

x = - \frac{1}{2 π} cos (2 π (t + 3)) + c_{1}

Wende die Anfangsbedingung an:

x = - \frac{1}{2 π} cos (2 π (t + 3)) + 1 + \frac{1}{2 π}

x = - \frac{1}{2 π} cos (2 π (t + 3)) + 1 + \frac{1}{2 π}

Graph

Beliebte Beispiele

tangent y=2x^2,(6,10)

t an g e n t y = 2 x^{2}, (6, 10)

f (x) = x^{l n (x)}

integral of 12x^2-7x+5

\int 12 x^{2} - 7 x + 5 d x

integral of t/(t^4+81)

\int \frac{t}{t ^{4} + 81} d t

fläche 1/(xsqrt(x^2-1)),x= 2/(sqrt(2)),x=2

a re a \frac{1}{x x ^{2} - 1}, x = \frac{2}{2}, x = 2