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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- 36 t} + e^{3 \frac{3}{4} t} (c_{2} cos (\frac{6 243 t}{4 ^{\frac{1}{3}}}) + c_{3} sin (\frac{6 243 t}{4 ^{\frac{1}{3}}}))

Schritte zur Lösung

y^{'''} (t) + 6 y = 0

Solve linear ODE:

y = c_{1} e^{- 36 t} + e^{3 \frac{3}{4} t} (c_{2} cos (\frac{6 243 t}{4 ^{\frac{1}{3}}}) + c_{3} sin (\frac{6 243 t}{4 ^{\frac{1}{3}}}))

y = c_{1} e^{- 36 t} + e^{3 \frac{3}{4} t} (c_{2} cos (\frac{6 243 t}{4 ^{\frac{1}{3}}}) + c_{3} sin (\frac{6 243 t}{4 ^{\frac{1}{3}}}))

Graph

Beliebte Beispiele

y^{''}+120y^'+10000y=0

y^{^{''}} + 120 y^{^{'}} + 10000 y = 0

4 y^{^{''}} = - 25 y

35y^{''''}+52y^{''}+9y=0

35 y^{^{''''}} + 52 y^{^{''}} + 9 y = 0

(d^4y)/(dt^4)-y^{'''}-y^{''}+y^'=0

\frac{d ^{4} y}{d t ^{4}} - y^{^{'''}} - y^{^{''}} + y^{^{'}} = 0

2u^{''}+u^'+3\H(t)=0

2 u^{^{''}} + u^{^{'}} + 3 H (t) = 0