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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{'''}+16y^'=e^{-pix}

y^{^{'''}} + 16 y^{^{'}} = e^{- π x}

x^{''}+4x=4sec^2(2t)

x^{^{''}} + 4 x = 4 sec^{2} (2 t)

y^{''}-6y^'+8y=2e^{3t},y(0)=0,y^'(0)=2

y^{^{''}} - 6 y^{^{'}} + 8 y = 2 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 2

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

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

y^{''}+y=cos(-t+pi/2),y(0)=0,y^'(0)=1

y^{^{''}} + y = cos (- t + \frac{π}{2}), y (0) = 0, y^{^{'}} (0) = 1