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Beliebt Rechnen >

x^{''}-2x^'+10x=7cos(t)

Lösung

x^{^{''}} - 2 x^{^{'}} + 10 x = 7 cos (t)

Lösung

x = e^{t} (c_{1} cos (3 t) + c_{2} sin (3 t)) - \frac{14}{85} sin (t) + \frac{63}{85} cos (t)

Schritte zur Lösung

x^{''} (t) - 2 x^{'} (t) + 10 x = 7 cos (t)

Solve linear ODE:

x = e^{t} (c_{1} cos (3 t) + c_{2} sin (3 t)) - \frac{14}{85} sin (t) + \frac{63}{85} cos (t)

x = e^{t} (c_{1} cos (3 t) + c_{2} sin (3 t)) - \frac{14}{85} sin (t) + \frac{63}{85} cos (t)

Graph

Beliebte Beispiele

y^{''}-y^'-6y=e^{2t},y^'(0)=1,y(0)=3

y^{^{''}} - y^{^{'}} - 6 y = e^{2 t}, y^{^{'}} (0) = 1, y (0) = 3

y^{''}-4y=14cos(2x)+21sin(2x)

y^{^{''}} - 4 y = 14 cos (2 x) + 21 sin (2 x)

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

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

y^{''}+3y^'+9y=8sin(6t)

y^{^{''}} + 3 y^{^{'}} + 9 y = 8 sin (6 t)

y^{''}-y^'+0.25y=3+e^{x/2}

y^{^{''}} - y^{^{'}} + 0.25 y = 3 + e^{\frac{x}{2}}