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Beliebt Rechnen >

y^{''}+2y^'-3y=0,y(0)=1,y^'(0)=-2

Lösung

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

Lösung

y = (1 - \frac{3}{4}) e^{t} + \frac{3}{4} e^{- 3 t}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = (1 - \frac{3}{4}) e^{t} + \frac{3}{4} e^{- 3 t}

y = (1 - \frac{3}{4}) e^{t} + \frac{3}{4} e^{- 3 t}

Graph

Beliebte Beispiele

77y^{''''}+204y^{''}+64y=0

77 y^{^{''''}} + 204 y^{^{''}} + 64 y = 0

3y^{''}-9y^'+6y=0

3 y^{^{''}} - 9 y^{^{'}} + 6 y = 0

(d^2y)/(dx^2)+10((dy)/(dx))+25y=0

\frac{d ^{2} y}{d x ^{2}} + 10 (\frac{d y}{d x}) + 25 y = 0

x^{''}+8x^'+80x=0

x^{^{''}} + 8 x^{^{'}} + 80 x = 0

y^{''}+4y^'+4y=0,y(-1)=5,y^'(-1)=4

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (- 1) = 5, y^{^{'}} (- 1) = 4