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Beliebt Rechnen >

y^{''}+3y^'+2y=1+3x+x^2

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = 1 + 3 x + x^{2}

Lösung

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + 2 y = 1 + 3 x + x^{2}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

Graph

Beliebte Beispiele

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

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

y^{''}+y^'-2y=6

y^{^{''}} + y^{^{'}} - 2 y = 6

y^{''}+3y^'+5y=4t+2+e^{7t}

y^{^{''}} + 3 y^{^{'}} + 5 y = 4 t + 2 + e^{7 t}

y^{'''}-y^{''}-16y^'+16y=3-e^x+e^{4x}

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} + 16 y = 3 - e^{x} + e^{4 x}

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

l in e a r y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x^{2} + 4 e^{4 x}