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Beliebt Rechnen >

y^{''}-4y^'+3y=0,y(0)= 3/5 ,y^'(0)= 1/5

Lösung

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = \frac{3}{5}, y^{^{'}} (0) = \frac{1}{5}

Lösung

y = (\frac{3}{5} - \frac{4}{5}) e^{3 t} + \frac{4}{5} e^{t}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 3 y = 0

Solve linear ODE:

y = (\frac{3}{5} - \frac{4}{5}) e^{3 t} + \frac{4}{5} e^{t}

y = (\frac{3}{5} - \frac{4}{5}) e^{3 t} + \frac{4}{5} e^{t}

Graph

Beliebte Beispiele

y^{''}-12y^'+36y=0,y(0)=5,y^'(0)=0

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + 3 y = 4 y^{^{'}}

y^{'''}+5y^{''}-34y^'-80y=0

y^{^{'''}} + 5 y^{^{''}} - 34 y^{^{'}} - 80 y = 0

y^{''}+1y=0,y(pi/2)=3,y^'(pi/2)=-1

y^{^{''}} + 1 y = 0, y (\frac{π}{2}) = 3, y^{^{'}} (\frac{π}{2}) = - 1

-2y^{''}-10y^'+5/2 y=0

- 2 y^{^{''}} - 10 y^{^{'}} + \frac{5}{2} y = 0