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Beliebt Rechnen >

y^{''}-3y^'+2y=0,y(0)=1,y^'(0)= 3/4

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{3}{4}

Lösung

y = (1 - \frac{5}{4}) e^{2 t} + \frac{5}{4} e^{t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = 0

Solve linear ODE:

y = (1 - \frac{5}{4}) e^{2 t} + \frac{5}{4} e^{t}

y = (1 - \frac{5}{4}) e^{2 t} + \frac{5}{4} e^{t}

Graph

Beliebte Beispiele

(D^{2} + 8 D + 16) y = 0

y^{^{''}} - \frac{1}{9} y = 0

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

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

77y^{''''}+156y^{''}+64y=0

77 y^{^{''''}} + 156 y^{^{''}} + 64 y = 0

y^{''}+4y^'+5y=0,y(pi/2)=0,y^'(pi/2)=2

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 2