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Beliebt Rechnen >

(d^2y)/(dx^2)+8(dy)/(dx)+16y=x^2+x+1

Lösung

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = x^{2} + x + 1

Lösung

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{x ^{2}}{16} + \frac{7}{128}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = x^{2} + x + 1

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{x ^{2}}{16} + \frac{7}{128}

y = c_{1} e^{- 4 x} + c_{2} x e^{- 4 x} + \frac{x ^{2}}{16} + \frac{7}{128}

Graph

Beliebte Beispiele

y^{'''}+y=2x^2+9

y^{^{'''}} + y = 2 x^{2} + 9

y^{'''}-y^'=3-7t

y^{^{'''}} - y^{^{'}} = 3 - 7 t

y^{'''}-5y^{''}-y^'+5y=e^{4x}

y^{^{'''}} - 5 y^{^{''}} - y^{^{'}} + 5 y = e^{4 x}

(D^{2} - D) y = 2 - 2 x

y^{''}-6y^'+8y=x,y(0)=0,y^'(0)=0

y^{^{''}} - 6 y^{^{'}} + 8 y = x, y (0) = 0, y^{^{'}} (0) = 0