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Beliebt Rechnen >

y^{''}-36y=12,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} - 36 y = 12, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = (- \frac{2}{3} + \frac{4}{3}) e^{6 t} + \frac{2}{3} e^{- 6 t} - \frac{1}{3}

Schritte zur Lösung

y^{''} (t) - 36 y = 12

Solve linear ODE:

y = (- \frac{2}{3} + \frac{4}{3}) e^{6 t} + \frac{2}{3} e^{- 6 t} - \frac{1}{3}

y = (- \frac{2}{3} + \frac{4}{3}) e^{6 t} + \frac{2}{3} e^{- 6 t} - \frac{1}{3}

Graph

Beliebte Beispiele

y^{''}+4y^'-y=k,y(0)=0,y^'(0)=0

y^{^{''}} + 4 y^{^{'}} - y = k, y (0) = 0, y^{^{'}} (0) = 0

(d^2y)/(dx^2)-25y=sinh(5x)

\frac{d ^{2} y}{d x ^{2}} - 25 y = sinh (5 x)

(D^2+1)y=sin^2(x)

(D^{2} + 1) y = sin^{2} (x)

y^{''}+6y^'+9y=-xe^4x

y^{^{''}} + 6 y^{^{'}} + 9 y = - x e^{4} x

1/2 y^{''}+10y=8cos(6t)

\frac{1}{2} y^{^{''}} + 10 y = 8 cos (6 t)