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Beliebt Rechnen >

y^{''}-9y^'+5y=xe^x

Lösung

y^{^{''}} - 9 y^{^{'}} + 5 y = x e^{x}

Lösung

y = c_{1} e^{\frac{( 9 + 61 ) x}{2}} + c_{2} e^{\frac{( 9 - 61 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{7}{9} e^{x}

Schritte zur Lösung

y^{''} (x) - 9 y^{'} (x) + 5 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{\frac{( 9 + 61 ) x}{2}} + c_{2} e^{\frac{( 9 - 61 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{7}{9} e^{x}

y = c_{1} e^{\frac{( 9 + 61 ) x}{2}} + c_{2} e^{\frac{( 9 - 61 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{7}{9} e^{x}

Graph

Beliebte Beispiele

4 y^{^{''}} - y^{^{'}} = 1

y^{''}+16y^'+64y=4sin(3x)

y^{^{''}} + 16 y^{^{'}} + 64 y = 4 sin (3 x)

y^{''}+7y^'+10y=15te^{4t}

y^{^{''}} + 7 y^{^{'}} + 10 y = 15 t e^{4 t}

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

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

y^{''}-y=t-2,y(2)=3,y^'(2)=0

y^{^{''}} - y = t - 2, y (2) = 3, y^{^{'}} (2) = 0