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Beliebt Rechnen >

(d^2y)/(dx^2)-4(dy)/(dx)+4y=x^3e^{2x}

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = x^{3} e^{2 x}

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{5}}{20}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = x^{3} e^{2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{5}}{20}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{5}}{20}

Graph

Beliebte Beispiele

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

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

y^{'''}+16y^'=e^{-pix}

y^{^{'''}} + 16 y^{^{'}} = e^{- π x}

x^{''}+4x=4sec^2(2t)

x^{^{''}} + 4 x = 4 sec^{2} (2 t)

y^{''}-6y^'+8y=2e^{3t},y(0)=0,y^'(0)=2

y^{^{''}} - 6 y^{^{'}} + 8 y = 2 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 2

y^{''}+4y^'+5y=e^xcos(2x)

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{x} cos (2 x)