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Beliebt Rechnen >

y^{''}-4y^'-5y=x^2

Lösung

y^{^{''}} - 4 y^{^{'}} - 5 y = x^{2}

Lösung

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{x ^{2}}{5} + \frac{8 x}{25} - \frac{42}{125}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) - 5 y = x^{2}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{x ^{2}}{5} + \frac{8 x}{25} - \frac{42}{125}

y = c_{1} e^{5 x} + c_{2} e^{- x} - \frac{x ^{2}}{5} + \frac{8 x}{25} - \frac{42}{125}

Graph

Beliebte Beispiele

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

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

y^{'''}+265y^'=tan(16x)

y^{^{'''}} + 265 y^{^{'}} = tan (16 x)

y^{''}-10y^'+9y=e^{2x}

y^{^{''}} - 10 y^{^{'}} + 9 y = e^{2 x}

y^{''}+y^'-6y=e^{2t}+t

y^{^{''}} + y^{^{'}} - 6 y = e^{2 t} + t

y^{'''}-3y^{''}-y^'+3y=1+e^x

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = 1 + e^{x}