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Beliebt Rechnen >

y^{''}+6y^'+13y=x^2

Lösung

y^{^{''}} + 6 y^{^{'}} + 13 y = x^{2}

Lösung

y = e^{- 3 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{2}}{13} - \frac{12 x}{169} + \frac{46}{2197}

Schritte zur Lösung

y^{''} (x) + 6 y^{'} (x) + 13 y = x^{2}

Solve linear ODE:

y = e^{- 3 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{2}}{13} - \frac{12 x}{169} + \frac{46}{2197}

y = e^{- 3 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{2}}{13} - \frac{12 x}{169} + \frac{46}{2197}

Graph

Beliebte Beispiele

y^{''}+9y=6cos(3x)+9sin(3x)

y^{^{''}} + 9 y = 6 cos (3 x) + 9 sin (3 x)

y^{'''}+7y^{''}+8y^'-16y=-2e^x-2

y^{^{'''}} + 7 y^{^{''}} + 8 y^{^{'}} - 16 y = - 2 e^{x} - 2

x^{'''}+3x^{''}+x^'+3x=t^2

x^{^{'''}} + 3 x^{^{''}} + x^{^{'}} + 3 x = t^{2}

y^{''}+3y^'+15.25y=e^t

y^{^{''}} + 3 y^{^{'}} + 15.25 y = e^{t}

y^{''}+5y=cos(7t)

y^{^{''}} + 5 y = cos (7 t)