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Beliebt Rechnen >

(d^2y)/(dx^2)+(dy)/(dx)4+8y=8x^2

Lösung

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

Lösung

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - x + \frac{1}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - x + \frac{1}{4}

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - x + \frac{1}{4}

Graph

Beliebte Beispiele

y^{''}-2y^'=x^2-1

y^{^{''}} - 2 y^{^{'}} = x^{2} - 1

1/4 y^{''}+y^'+y=sin(x)

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = sin (x)

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

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

y^{''}-7y^'+12y=-288t^3

y^{^{''}} - 7 y^{^{'}} + 12 y = - 288 t^{3}

y^{^{''}} + y = - 3