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Beliebt Rechnen >

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

Lösung

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

Lösung

x = c_{1} e^{t} + c_{2} e^{- 5 t} - \frac{4 t ^{2}}{5} - \frac{32 t}{25} - \frac{168}{125}

Schritte zur Lösung

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

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- 5 t} - \frac{4 t ^{2}}{5} - \frac{32 t}{25} - \frac{168}{125}

x = c_{1} e^{t} + c_{2} e^{- 5 t} - \frac{4 t ^{2}}{5} - \frac{32 t}{25} - \frac{168}{125}

Graph

Beliebte Beispiele

2y^{''}+2y^'+5y=cos(x)-5sin(x)

2 y^{^{''}} + 2 y^{^{'}} + 5 y = cos (x) - 5 sin (x)

y^{''}-4y=xe^{-x}

y^{^{''}} - 4 y = x e^{- x}

4(d^2y)/(dx^2)-y=xe^{x/2}

4 \frac{d ^{2} y}{d x ^{2}} - y = x e^{\frac{x}{2}}

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

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

y^{''}+y=4sin(3x)

y^{^{''}} + y = 4 sin (3 x)