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Beliebt Rechnen >

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

Lösung

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

Lösung

y = (5 - \frac{15}{4}) e^{\frac{3 t}{2}} + \frac{15}{4} e^{- \frac{t}{2}}

Schritte zur Lösung

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

Solve linear ODE:

y = (5 - \frac{15}{4}) e^{\frac{3 t}{2}} + \frac{15}{4} e^{- \frac{t}{2}}

y = (5 - \frac{15}{4}) e^{\frac{3 t}{2}} + \frac{15}{4} e^{- \frac{t}{2}}

Graph

Beliebte Beispiele

y^{''}+9y=0,y(0)=2,y^'(0)=1

y^{^{''}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 1

(D^2-2D+5)^2y=0

(D^{2} - 2 D + 5)^{2} y = 0

y^{''}+6y^'+8.96y=0

y^{^{''}} + 6 y^{^{'}} + 8.96 y = 0

y^{''}+2y^'+1.25y=0

y^{^{''}} + 2 y^{^{'}} + 1.25 y = 0

y^{''}+20y^'+36y=0,y(0)=3,y^'(0)=0

y^{^{''}} + 20 y^{^{'}} + 36 y = 0, y (0) = 3, y^{^{'}} (0) = 0