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Beliebt Rechnen >

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

Lösung

linear

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=8xe^x-6

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 x e^{x} - 6

y^{''}+3y^'-10y=e^{-5x}

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{- 5 x}

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

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

y^{''}-2y^'-3y=x+2

y^{^{''}} - 2 y^{^{'}} - 3 y = x + 2

x^{''}+x=tan(t)

x^{^{''}} + x = tan (t)