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Beliebt Rechnen >

y^{''}-16y=0,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} - 16 y = 0, y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = \frac{1}{8} e^{4 t} - \frac{1}{8} e^{- 4 t}

Schritte zur Lösung

y^{''} (t) - 16 y = 0

Solve linear ODE:

y = \frac{1}{8} e^{4 t} - \frac{1}{8} e^{- 4 t}

y = \frac{1}{8} e^{4 t} - \frac{1}{8} e^{- 4 t}

Graph

Beliebte Beispiele

y^{''}-7y^'=0,y(0)=2-2e^7,y(1)=0

y^{^{''}} - 7 y^{^{'}} = 0, y (0) = 2 - 2 e^{7}, y (1) = 0

(d^2y)/(dx^2)+15(dy)/(dx)+56y=0

\frac{d ^{2} y}{d x ^{2}} + 15 \frac{d y}{d x} + 56 y = 0

y^{''}+4y^'+ky=0

y^{^{''}} + 4 y^{^{'}} + k y = 0

y^{''}+4y=0,y(0)=6,y^'(0)=-6

y^{^{''}} + 4 y = 0, y (0) = 6, y^{^{'}} (0) = - 6

y^{''}+7y^'+20y=0

y^{^{''}} + 7 y^{^{'}} + 20 y = 0