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Beliebt Rechnen >

y^{''}+6y^'=1-3x+x^2

Lösung

y^{^{''}} + 6 y^{^{'}} = 1 - 3 x + x^{2}

Lösung

y = c_{1} + c_{2} e^{- 6 x} + \frac{x ^{3}}{18} - \frac{5 x ^{2}}{18} + \frac{7 x}{27}

Schritte zur Lösung

y^{''} (x) + 6 y^{'} (x) = 1 - 3 x + x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 6 x} + \frac{x ^{3}}{18} - \frac{5 x ^{2}}{18} + \frac{7 x}{27}

y = c_{1} + c_{2} e^{- 6 x} + \frac{x ^{3}}{18} - \frac{5 x ^{2}}{18} + \frac{7 x}{27}

Graph

Beliebte Beispiele

x^{''}+8x^'+16x=8sin(4t)

x^{^{''}} + 8 x^{^{'}} + 16 x = 8 sin (4 t)

y^{'''}+y^{''}=5x^2

y^{^{'''}} + y^{^{''}} = 5 x^{2}

y^{''}-4y^'+4y=t^3

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3}

(d^2y)/(dx^2)-6(dy)/(dx)+9y=(x+1)e^x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = (x + 1) e^{x}

y^{''}-4y^'+2y=5e^x

y^{^{''}} - 4 y^{^{'}} + 2 y = 5 e^{x}