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Beliebt Rechnen >

y^{''}-8y^'+16y=(x-1)e^{4x}

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = (x - 1) e^{4 x}

Lösung

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{e ^{4 x} x ^{3}}{6} - \frac{e ^{4 x} x ^{2}}{2}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = (x - 1) e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{e ^{4 x} x ^{3}}{6} - \frac{e ^{4 x} x ^{2}}{2}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{e ^{4 x} x ^{3}}{6} - \frac{e ^{4 x} x ^{2}}{2}

Graph

Beliebte Beispiele

y^{''}-5y^'-14y=e^x(x+1)

y^{^{''}} - 5 y^{^{'}} - 14 y = e^{x} (x + 1)

linear y^{''}+4y=e^{3t},y(0)=0,y^'(0)=0

l in e a r y^{^{''}} + 4 y = e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0

(D^3+D^2+D+1)y=xe^x

(D^{3} + D^{2} + D + 1) y = x e^{x}

30y^{''}+25y^'+4y=40

30 y^{^{''}} + 25 y^{^{'}} + 4 y = 40

y^{''}-y=sec^3(x)-sec(x)

y^{^{''}} - y = sec^{3} (x) - sec (x)