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Beliebt Rechnen >

-a*y^{''}+y^'=0,y(0)=1,y(1)=0

Lösung

- a \cdot y^{^{''}} + y^{^{'}} = 0, y (0) = 1, y (1) = 0

Lösung

y = 1 + \frac{1}{- 1 + e ^{\frac{1}{a}}} - \frac{e ^{\frac{t}{a}}}{- 1 + e ^{\frac{1}{a}}}

Schritte zur Lösung

- a \cdot y^{''} (t) + y^{'} (t) = 0

Solve linear ODE:

y = 1 + \frac{1}{- 1 + e ^{\frac{1}{a}}} - \frac{e ^{\frac{t}{a}}}{- 1 + e ^{\frac{1}{a}}}

y = 1 + \frac{1}{- 1 + e ^{\frac{1}{a}}} - \frac{e ^{\frac{t}{a}}}{- 1 + e ^{\frac{1}{a}}}

Graph

Beliebte Beispiele

16y^{''}+9y^'=0

16 y^{^{''}} + 9 y^{^{'}} = 0

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

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

49y^{''}+42y^'+9y=0,y(0)=7,y^'(0)=1

49 y^{^{''}} + 42 y^{^{'}} + 9 y = 0, y (0) = 7, y^{^{'}} (0) = 1

y^{''''}-6y^{'''}+5y^{''}=0

y^{^{''''}} - 6 y^{^{'''}} + 5 y^{^{''}} = 0

-2y^{''}+6y^'+5y=0

- 2 y^{^{''}} + 6 y^{^{'}} + 5 y = 0