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Beliebt Rechnen >

4y^{''}-y=0,y(-9)=1,y^'(-9)=-1

Lösung

4 y^{^{''}} - y = 0, y (- 9) = 1, y^{^{'}} (- 9) = - 1

Lösung

y = (e^{\frac{9}{2}} - \frac{3 e ^{\frac{9}{2}}}{2}) e^{\frac{t}{2}} + \frac{3 e ^{\frac{- t - 9}{2}}}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = (e^{\frac{9}{2}} - \frac{3 e ^{\frac{9}{2}}}{2}) e^{\frac{t}{2}} + \frac{3 e ^{\frac{- t - 9}{2}}}{2}

y = (e^{\frac{9}{2}} - \frac{3 e ^{\frac{9}{2}}}{2}) e^{\frac{t}{2}} + \frac{3 e ^{\frac{- t - 9}{2}}}{2}

Graph

Beliebte Beispiele

1/16 y^{''}+y^'+2y=0

\frac{1}{16} y^{^{''}} + y^{^{'}} + 2 y = 0

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

y^{^{''}} + y^{^{'}} + \frac{1}{3} y = 0

4y^{''}+12y^'+9y=0,y(0)=2,y^'(0)=-1

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

x^{''}+3x^'-3x=0

x^{^{''}} + 3 x^{^{'}} - 3 x = 0

y^{''}+8y^'+160y=0

y^{^{''}} + 8 y^{^{'}} + 160 y = 0