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Beliebt Rechnen >

1296y^{''}+72y^'+y=0,y(0)=7,y^'(0)=5

Lösung

1296 y^{^{''}} + 72 y^{^{'}} + y = 0, y (0) = 7, y^{^{'}} (0) = 5

Lösung

y = 7 e^{- \frac{t}{36}} + \frac{187 e ^{- \frac{t}{36}} t}{36}

Schritte zur Lösung

1296 y^{''} (t) + 72 y^{'} (t) + y = 0

Solve linear ODE:

y = 7 e^{- \frac{t}{36}} + \frac{187 e ^{- \frac{t}{36}} t}{36}

y = 7 e^{- \frac{t}{36}} + \frac{187 e ^{- \frac{t}{36}} t}{36}

Graph

Beliebte Beispiele

y^{''}-16y=0,y(0)=13,y^'(0)=20

y^{^{''}} - 16 y = 0, y (0) = 13, y^{^{'}} (0) = 20

y^{''}+6y^'+5y=0,y(0)=0,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 0

2y^{'''}+7y^{''}-17y^'-10y=0

2 y^{^{'''}} + 7 y^{^{''}} - 17 y^{^{'}} - 10 y = 0

1y^{''}+3y^'+2y=0

1 y^{^{''}} + 3 y^{^{'}} + 2 y = 0

2y^{''''}+4y^{''}+2y=0

2 y^{^{''''}} + 4 y^{^{''}} + 2 y = 0