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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y=3sin(x)+cos(3x)

y^{^{''}} + 4 y = 3 sin (x) + cos (3 x)

y^{''}+5y^'+4y=3-2x

y^{^{''}} + 5 y^{^{'}} + 4 y = 3 - 2 x

(d^2y)/(dx^2)-6(dy)/(dx)+9y=54x+18

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 54 x + 18

y^{'''}-6y^{''}+12y^'-8y=5e^{2x}

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 5 e^{2 x}

y^{''}-y^'-2y=7x+4

y^{^{''}} - y^{^{'}} - 2 y = 7 x + 4