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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{3 x} x ^{2}}{4} - \frac{e ^{3 x} x}{2} + \frac{3}{8} e^{3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{3 x} x ^{2}}{4} - \frac{e ^{3 x} x}{2} + \frac{3}{8} e^{3 x}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{3 x} x ^{2}}{4} - \frac{e ^{3 x} x}{2} + \frac{3}{8} e^{3 x}

Graph

Beliebte Beispiele

(d^2-1)y=xsin(x)+(1+x^2)e^x

(d^{2} - 1) y = x sin (x) + (1 + x^{2}) e^{x}

3x^{''}-30x^'+75x=2t+1

3 x^{^{''}} - 30 x^{^{'}} + 75 x = 2 t + 1

y^{''}+y^'-6y=12e^{3t}+12e^{-2t}

y^{^{''}} + y^{^{'}} - 6 y = 12 e^{3 t} + 12 e^{- 2 t}

y^{''}+10y^'+16y=2581cos(5t)

y^{^{''}} + 10 y^{^{'}} + 16 y = 2581 cos (5 t)

y^{^{''}} = k y - c