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Beliebt Rechnen >

y^{''}+8y^'+20y=0,y(0)=15,y^'(0)=-6

Lösung

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 15, y^{^{'}} (0) = - 6

Lösung

y = e^{- 4 t} (15 cos (2 t) + 27 sin (2 t))

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 20 y = 0

Solve linear ODE:

y = e^{- 4 t} (15 cos (2 t) + 27 sin (2 t))

y = e^{- 4 t} (15 cos (2 t) + 27 sin (2 t))

Graph

Beliebte Beispiele

y^{''}+y=0,y^'(pi/2)=0,y^'(0)=0

y^{^{''}} + y = 0, y^{^{'}} (\frac{π}{2}) = 0, y^{^{'}} (0) = 0

y^{''}-4y^'-2y=0

y^{^{''}} - 4 y^{^{'}} - 2 y = 0

y^{''}-6y^'-6y=0

y^{^{''}} - 6 y^{^{'}} - 6 y = 0

(d^2y)/(dx^2)+3(dy)/(dx)+2y=0

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = 0

y^{''}+y=0,y(pi/3)=2,y^'(pi/3)=-4

y^{^{''}} + y = 0, y (\frac{π}{3}) = 2, y^{^{'}} (\frac{π}{3}) = - 4