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Beliebt Rechnen >

(d^2y)/(dx^2)+(dy)/(dx)4+8y=8x^2+8x+1

Lösung

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2} + 8 x + 1

Lösung

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - \frac{1}{8}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2} + 8 x + 1

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - \frac{1}{8}

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x^{2} - \frac{1}{8}

Graph

Beliebte Beispiele

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

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

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