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Beliebt Rechnen >

y^{''}-y=sin(t),y(0)=0,y^'(0)=1

Lösung

y^{^{''}} - y = sin (t), y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = \frac{3}{4} e^{t} - \frac{3}{4} e^{- t} - \frac{1}{2} sin (t)

Schritte zur Lösung

y^{''} (t) - y = sin (t)

Solve linear ODE:

y = \frac{3}{4} e^{t} - \frac{3}{4} e^{- t} - \frac{1}{2} sin (t)

y = \frac{3}{4} e^{t} - \frac{3}{4} e^{- t} - \frac{1}{2} sin (t)

Graph

Beliebte Beispiele

y^{''}+6y^'+9y=2sin(x)

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 sin (x)

y^{''}-8y^'+16y=8e^{4x}

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 e^{4 x}

y^{''}+2y^'+y=(e^{-x})/(x^2+1)

y^{^{''}} + 2 y^{^{'}} + y = \frac{e ^{- x}}{x ^{2} + 1}

y^{''}-2y^'+17y=e^xcos(4x)

y^{^{''}} - 2 y^{^{'}} + 17 y = e^{x} cos (4 x)

y^{'''}-4y^'=xe^{2x}+x^2+sin(x)

y^{^{'''}} - 4 y^{^{'}} = x e^{2 x} + x^{2} + sin (x)