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Beliebt Rechnen >

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

Lösung

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

Lösung

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{4 t ^{2}}{5} - \frac{16 t}{25} - \frac{8}{125}

Schritte zur Lösung

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

Solve linear ODE:

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{4 t ^{2}}{5} - \frac{16 t}{25} - \frac{8}{125}

x = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{4 t ^{2}}{5} - \frac{16 t}{25} - \frac{8}{125}

Graph

Beliebte Beispiele

y^{''}-y^'-2y=1-x

y^{^{''}} - y^{^{'}} - 2 y = 1 - x

y^{'''}-5y^{''}+6y^'=3+7x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 3 + 7 x

y^{''}-y=(e^{2x}-e^{-2x})/2

y^{^{''}} - y = \frac{e ^{2 x} - e ^{- 2 x}}{2}

y^{''}+y=1-1-\H(pi/2*t)

y^{^{''}} + y = 1 - 1 - H (\frac{π}{2} \cdot t)

y^{''}+11y=2e^{7x}

y^{^{''}} + 11 y = 2 e^{7 x}