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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{^{'''}} + y^{^{'}} = 4 x

(d^2y)/(dx^2)-2(dy)/(dx)=(e^x)/(x^2+1)

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

(d^2y)/(dx^2)-3(dy)/(dx)+2y=e^{3x}

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = e^{3 x}

y^{''}+3y^'-40y=-132t+80t^2

y^{^{''}} + 3 y^{^{'}} - 40 y = - 132 t + 80 t^{2}

y^{''}+8y^'+12=0

y^{^{''}} + 8 y^{^{'}} + 12 = 0