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Beliebt Rechnen >

y^{'''}-4y^{''}+5y^'-2y=2e^{-x}+cos(x)

Lösung

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 2 e^{- x} + cos (x)

Lösung

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} x e^{x} - \frac{1}{6} e^{- x} + \frac{1}{5} sin (x) + \frac{1}{10} cos (x)

Schritte zur Lösung

y^{'''} (x) - 4 y^{''} (x) + 5 y^{'} (x) - 2 y = 2 e^{- x} + cos (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} x e^{x} - \frac{1}{6} e^{- x} + \frac{1}{5} sin (x) + \frac{1}{10} cos (x)

y = c_{1} e^{2 x} + c_{2} e^{x} + c_{3} x e^{x} - \frac{1}{6} e^{- x} + \frac{1}{5} sin (x) + \frac{1}{10} cos (x)

Graph

Beliebte Beispiele

1/4 y^{''}+y^{''}+y=x^2-2x

\frac{1}{4} y^{^{''}} + y^{^{''}} + y = x^{2} - 2 x

y^{''}+3y^'+2y=1,2e^ty(0)=2,y^'(0)=3

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, 2 e^{t} y (0) = 2, y^{^{'}} (0) = 3

y^{''}+y^'=e^x+x^3

y^{^{''}} + y^{^{'}} = e^{x} + x^{3}

y^{''}+ky=8sin(t)

y^{^{''}} + k y = 8 sin (t)

y^{''}+2y^'-3y=5e^{2x},y(0)=1,y^'(0)=a

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = a