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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y=e^x(6-x)

y^{^{''}} + y = e^{x} (6 - x)

x^{''}+6x^'+9x=10cos(2t)

x^{^{''}} + 6 x^{^{'}} + 9 x = 10 cos (2 t)

y^{'''}+2y^'=3(y^{''}-x^2+2)

y^{^{'''}} + 2 y^{^{'}} = 3 (y^{^{''}} - x^{2} + 2)

y^{''}-4y^'+3y=3+3x,y(0)=1,y^'(0)=3

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 + 3 x, y (0) = 1, y^{^{'}} (0) = 3

y^{'''}-3y^'-2y=e^x(xe^x+1)

y^{^{'''}} - 3 y^{^{'}} - 2 y = e^{x} (x e^{x} + 1)