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Beliebt Rechnen >

25y^{''}-100y^'+109y=0,y(0)=9,y^'(0)=8

Lösung

25 y^{^{''}} - 100 y^{^{'}} + 109 y = 0, y (0) = 9, y^{^{'}} (0) = 8

Lösung

y = e^{2 t} (9 cos (\frac{3 t}{5}) - \frac{50}{3} sin (\frac{3 t}{5}))

Schritte zur Lösung

25 y^{''} (t) - 100 y^{'} (t) + 109 y = 0

Solve linear ODE:

y = e^{2 t} (9 cos (\frac{3 t}{5}) - \frac{50}{3} sin (\frac{3 t}{5}))

y = e^{2 t} (9 cos (\frac{3 t}{5}) - \frac{50}{3} sin (\frac{3 t}{5}))

Graph

Beliebte Beispiele

256y^{''''}=81y

256 y^{^{''''}} = 81 y

3 y^{^{''}} + 15 y = 0

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

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

1/4 x^{''}+10x^'+1000x=0

\frac{1}{4} x^{^{''}} + 10 x^{^{'}} + 1000 x = 0

4y^{'''}-7y^{''}-34y^'-8y=0

4 y^{^{'''}} - 7 y^{^{''}} - 34 y^{^{'}} - 8 y = 0