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Beliebt Rechnen >

2x^{''}+5x^'+2x=4e-2t-t

Lösung

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 4 e - 2 t - t

Lösung

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - \frac{3 t}{2} + \frac{8 e + 15}{4}

Schritte zur Lösung

2 x^{''} (t) + 5 x^{'} (t) + 2 x = 4 e - 2 t - t

Solve linear ODE:

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - \frac{3 t}{2} + \frac{8 e + 15}{4}

x = c_{1} e^{- \frac{t}{2}} + c_{2} e^{- 2 t} - \frac{3 t}{2} + \frac{8 e + 15}{4}

Graph

Beliebte Beispiele

y^{'''}-11y^{''}+28y^'=90e^x

y^{^{'''}} - 11 y^{^{''}} + 28 y^{^{'}} = 90 e^{x}

y^{''}+y^'=arctan(x)

y^{^{''}} + y^{^{'}} = arctan (x)

y^{''}+2y^'-8y=8x^2-3

y^{^{''}} + 2 y^{^{'}} - 8 y = 8 x^{2} - 3

(d^2y)/(dx^2)+y=-16*cos(3x)

\frac{d ^{2} y}{d x ^{2}} + y = - 16 \cdot cos (3 x)

(D-2)^2y=20-3xe^2x

(D - 2)^{2} y = 20 - 3 x e^{2} x