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Beliebt Rechnen >

y^{''}+3y^'-4y=2,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = (\frac{1}{10} + \frac{1}{2}) e^{t} - \frac{1}{10} e^{- 4 t} - \frac{1}{2}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) - 4 y = 2

Solve linear ODE:

y = (\frac{1}{10} + \frac{1}{2}) e^{t} - \frac{1}{10} e^{- 4 t} - \frac{1}{2}

y = (\frac{1}{10} + \frac{1}{2}) e^{t} - \frac{1}{10} e^{- 4 t} - \frac{1}{2}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+4y=x-sin(3x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = x - sin (3 x)

y^{''}-3y^'+2y=xcos(2x)

y^{^{''}} - 3 y^{^{'}} + 2 y = x cos (2 x)

y^{''}-y^'-64y=54cos(3x)

y^{^{''}} - y^{^{'}} - 64 y = 54 cos (3 x)

y^{'''}-5y^'+6y^'=9+5sin(x)

y^{^{'''}} - 5 y^{^{'}} + 6 y^{^{'}} = 9 + 5 sin (x)

(d+2)(d-1)^2y=e^{-2}x+2sinh(x)

(d + 2) (d - 1)^{2} y = e^{- 2} x + 2 sinh (x)