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Beliebt Rechnen >

y^{''}-y=e^tcos(t),y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - y = e^{t} cos (t), y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = \frac{1}{5} e^{- t} + \frac{2}{5} e^{t} sin (t) - \frac{1}{5} e^{t} cos (t)

Schritte zur Lösung

y^{''} (t) - y = e^{t} cos (t)

Solve linear ODE:

y = \frac{1}{5} e^{- t} + \frac{2}{5} e^{t} sin (t) - \frac{1}{5} e^{t} cos (t)

y = \frac{1}{5} e^{- t} + \frac{2}{5} e^{t} sin (t) - \frac{1}{5} e^{t} cos (t)

Graph

Beliebte Beispiele

y^{''}+y=1,y(0)=2,y^'(0)=1

y^{^{''}} + y = 1, y (0) = 2, y^{^{'}} (0) = 1

y^{''}-2y^'+y=t^{-4}e^t

y^{^{''}} - 2 y^{^{'}} + y = t^{- 4} e^{t}

y^{''}-2y^'-3y=x-e^x

y^{^{''}} - 2 y^{^{'}} - 3 y = x - e^{x}

(d^2y)/(dx^2)-6y=e^{3x}(x^2+2)

\frac{d ^{2} y}{d x ^{2}} - 6 y = e^{3 x} (x^{2} + 2)

2y^{''}+y^'+2y=1,y(0)=0,y^'(0)=0

2 y^{^{''}} + y^{^{'}} + 2 y = 1, y (0) = 0, y^{^{'}} (0) = 0