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Beliebt Rechnen >

x^{''}+2x^'+3x=t^2+4t

Lösung

x^{^{''}} + 2 x^{^{'}} + 3 x = t^{2} + 4 t

Lösung

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{t ^{2}}{3} + \frac{8 t}{9} - \frac{22}{27}

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 3 x = t^{2} + 4 t

Solve linear ODE:

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{t ^{2}}{3} + \frac{8 t}{9} - \frac{22}{27}

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{t ^{2}}{3} + \frac{8 t}{9} - \frac{22}{27}

Graph

Beliebte Beispiele

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

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

2y^{''}+3y^'+y=gt

2 y^{^{''}} + 3 y^{^{'}} + y = g t

y^{''}-y=2t,y(0)=-2t

y^{^{''}} - y = 2 t, y (0) = - 2 t

y^{''}=-3y+cos(sqrt(3)x)

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

y^{''}-y^'-6y=62cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 62 cos (3 x)