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Beliebt Rechnen >

y^{''}+4y^'+4y=3t

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 t

Lösung

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{3 t}{4} - \frac{3}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{3 t}{4} - \frac{3}{4}

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} + \frac{3 t}{4} - \frac{3}{4}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+2(dy)/(dx)-3y=24e^{3x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 24 e^{3 x}

y^{''}-y^'-2y=8sin(t)-2cos(t)

y^{^{''}} - y^{^{'}} - 2 y = 8 sin (t) - 2 cos (t)

y^{''}+6y^'+13y=13x^2

y^{^{''}} + 6 y^{^{'}} + 13 y = 13 x^{2}

2y^{''}-y^'-y=t+1,y(0)=1,y^'(0)=0

2 y^{^{''}} - y^{^{'}} - y = t + 1, y (0) = 1, y^{^{'}} (0) = 0

y^{''}+4y=sin(x)-cos(x)

y^{^{''}} + 4 y = sin (x) - cos (x)