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Beliebt Rechnen >

(d^2y)/(dx^2)+4(dy)/(dx)+5y=x*e^{2x}

Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x \cdot e^{2 x}

Lösung

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{2 x} x}{17} - \frac{8}{289} e^{2 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x \cdot e^{2 x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{2 x} x}{17} - \frac{8}{289} e^{2 x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{2 x} x}{17} - \frac{8}{289} e^{2 x}

Graph

Beliebte Beispiele

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

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

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

y^{''}-4y^'+4y=(x+1)e^x

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) e^{x}

y^{''}-y^'=e^2x,y(0)=0,y(1)=0

y^{^{''}} - y^{^{'}} = e^{2} x, y (0) = 0, y (1) = 0

y^{''}-4y=sin(x)

y^{^{''}} - 4 y = sin (x)