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Beliebt Rechnen >

(d^2y)/(dx^2)-8(dy)/(dx)+16y=e^{4x}

Lösung

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 16 y = e^{4 x}

Lösung

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{e ^{4 x} x ^{2}}{2}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 16 y = e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{e ^{4 x} x ^{2}}{2}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{e ^{4 x} x ^{2}}{2}

Graph

Beliebte Beispiele

y^{''}+y=5xsin(x)

y^{^{''}} + y = 5 x sin (x)

y^{''}-y^'-2y=cosh(2t)

y^{^{''}} - y^{^{'}} - 2 y = cosh (2 t)

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

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

y^{''}+3y^'+2y=e^{-t},y(4)=1,y^'(4)=3

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- t}, y (4) = 1, y^{^{'}} (4) = 3

y^{''}+25y=2xcos(5x)

y^{^{''}} + 25 y = 2 x cos (5 x)