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Beliebt Rechnen >

y^{''}-4y^'-12y=2t^3-t+3

Lösung

y^{^{''}} - 4 y^{^{'}} - 12 y = 2 t^{3} - t + 3

Lösung

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t ^{3}}{6} + \frac{t ^{2}}{6} - \frac{t}{9} - \frac{5}{27}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 12 y = 2 t^{3} - t + 3

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t ^{3}}{6} + \frac{t ^{2}}{6} - \frac{t}{9} - \frac{5}{27}

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t ^{3}}{6} + \frac{t ^{2}}{6} - \frac{t}{9} - \frac{5}{27}

Graph

Beliebte Beispiele

y^{''}+y^'+y=x*e^x

y^{^{''}} + y^{^{'}} + y = x \cdot e^{x}

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

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

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

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

2y^{''}-7y^'+5y=-29

2 y^{^{''}} - 7 y^{^{'}} + 5 y = - 29

y^{''}+8y^'+16y=e^{-4t}

y^{^{''}} + 8 y^{^{'}} + 16 y = e^{- 4 t}