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Beliebt Rechnen >

y^{''}-4y^'-12y=t-6

Lösung

y^{^{''}} - 4 y^{^{'}} - 12 y = t - 6

Lösung

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t}{12} + \frac{19}{36}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 12 y = t - 6

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t}{12} + \frac{19}{36}

y = c_{1} e^{6 t} + c_{2} e^{- 2 t} - \frac{t}{12} + \frac{19}{36}

Graph

Beliebte Beispiele

y^{''}-6y^'+5y=sin(4x),y(0)=1,y^'(0)=-4

y^{^{''}} - 6 y^{^{'}} + 5 y = sin (4 x), y (0) = 1, y^{^{'}} (0) = - 4

x^{^{''}} + 4 x = e

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

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

(d^2y)/(dx^2)=(dy)/(dx)+x

\frac{d ^{2} y}{d x ^{2}} = \frac{d y}{d x} + x

y^{''}+9y=6*sin(3x)-6*cos(-3x)+36*e^{3x}

y^{^{''}} + 9 y = 6 \cdot sin (3 x) - 6 \cdot cos (- 3 x) + 36 \cdot e^{3 x}