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Beliebt Rechnen >

y^{''}-6y^'+9y=3x^2+4e^{4x}

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}

Lösung

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{x ^{2}}{3} + \frac{4 x + 2}{9} + 4 e^{4 x}

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 9 y = 3 x^{2} + 4 e^{4 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{x ^{2}}{3} + \frac{4 x + 2}{9} + 4 e^{4 x}

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{x ^{2}}{3} + \frac{4 x + 2}{9} + 4 e^{4 x}

Graph

Beliebte Beispiele

y^{''}+4y^'+3y=e^{-3x}

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- 3 x}

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

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

v^{''}-16v=2e^{4x}

v^{^{''}} - 16 v = 2 e^{4 x}

y^{''}+2y^'+y=t^5e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = t^{5} e^{- t}

y^{''}+49y=17sec^2(7t)

y^{^{''}} + 49 y = 17 sec^{2} (7 t)