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Beliebt Rechnen >

(d^2y)/(dx^2)-4y=8x^2-x+12

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 y = 8 x^{2} - x + 12

Lösung

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 y = 8 x^{2} - x + 12

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{'''}+5y^{''}-14=0

y^{^{'''}} + 5 y^{^{''}} - 14 = 0

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

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

x^{''}-6x^'+9x=e^{3t}

x^{^{''}} - 6 x^{^{'}} + 9 x = e^{3 t}

y^{''}+100y^'+2500y=30,y(0)=0,y^'(0)=2

y^{^{''}} + 100 y^{^{'}} + 2500 y = 30, y (0) = 0, y^{^{'}} (0) = 2

linear (d^2x)/(dt^2)+x=6cos(2t),x(0)=3

l in e a r \frac{d ^{2} x}{d t ^{2}} + x = 6 cos (2 t), x (0) = 3