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Beliebt Rechnen >

y^{''}-2y^'-8y=2sin(x)+(12x-10)e^{4x}

Lösung

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 sin (x) + (12 x - 10) e^{4 x}

Lösung

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{18}{85} sin (x) + \frac{4}{85} cos (x) + e^{4 x} x^{2} - 2 e^{4 x} x

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 8 y = 2 sin (x) + (12 x - 10) e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{18}{85} sin (x) + \frac{4}{85} cos (x) + e^{4 x} x^{2} - 2 e^{4 x} x

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{18}{85} sin (x) + \frac{4}{85} cos (x) + e^{4 x} x^{2} - 2 e^{4 x} x

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-3(dy)/(dx)-4y=2sin(x)

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} - 4 y = 2 sin (x)

y^{''}+16y=-8sin(4x)+17e^x

y^{^{''}} + 16 y = - 8 sin (4 x) + 17 e^{x}

y^{''}+2y^'+17y=-44-85x

y^{^{''}} + 2 y^{^{'}} + 17 y = - 44 - 85 x

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

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

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

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