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Beliebt Rechnen >

(dy)/(dt)-y=2cos(kt),y(0)=7

Lösung

\frac{d y}{d t} - y = 2 cos (k t), y (0) = 7

Lösung

y = \frac{2 e ^{t} ( k e ^{- t} sin ( k t ) - e ^{- t} cos ( k t ) )}{k ^{2} + 1} + (7 + \frac{2}{k ^{2} + 1}) e^{t}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{2 e ^{t} ( k e ^{- t} sin ( k t ) - e ^{- t} cos ( k t ) )}{k ^{2} + 1} + (7 + \frac{2}{k ^{2} + 1}) e^{t}

y = \frac{2 e ^{t} ( k e ^{- t} sin ( k t ) - e ^{- t} cos ( k t ) )}{k ^{2} + 1} + (7 + \frac{2}{k ^{2} + 1}) e^{t}

Graph

Beliebte Beispiele

(dy)/(dx)=1+x^2+y^2+x^2y^2

\frac{d y}{d x} = 1 + x^{2} + y^{2} + x^{2} y^{2}

derivative of sqrt(x-2\sqrt{x-2)}

\frac{d}{d x} (x - 2 x - 2)

derivative of (1+x^{1/2})

\frac{d}{d x} ((1 + x)^{\frac{1}{2}})

derivative of x^2-x-ln(x)

\frac{d}{d x} (x^{2} - x - ln (x))

integral from-1 to 2 of (8-x^2)

\int_{- 1}^{2} (8 - x^{2}) d x