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Beliebt Rechnen >

y^{''}+4y^'+13y=0,y(0)=1,y^'(0)=2

Lösung

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 2

Lösung

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

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 13 y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-4y^'-5y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

x^{''}+4x=0,x(0)=8,x^'(0)=-13

x^{^{''}} + 4 x = 0, x (0) = 8, x^{^{'}} (0) = - 13

4y^{''}+9y^'-9y=0

4 y^{^{''}} + 9 y^{^{'}} - 9 y = 0

(d^3-5d^2+4d-20)x=0

(d^{3} - 5 d^{2} + 4 d - 20) x = 0

(y^{''})/y =-a^2

\frac{y ^{^{''}}}{y} = - a^{2}