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Beliebt Rechnen >

1/4 y^{''}+y^{''}+y=x^2-2x

Lösung

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

Lösung

y = c_{1} cos (\frac{2 x}{5}) + c_{2} sin (\frac{2 x}{5}) + x^{2} - 2 x - \frac{5}{2}

Schritte zur Lösung

\frac{1}{4} y^{''} (x) + y^{''} (x) + y = x^{2} - 2 x

Solve linear ODE:

y = c_{1} cos (\frac{2 x}{5}) + c_{2} sin (\frac{2 x}{5}) + x^{2} - 2 x - \frac{5}{2}

y = c_{1} cos (\frac{2 x}{5}) + c_{2} sin (\frac{2 x}{5}) + x^{2} - 2 x - \frac{5}{2}

Graph

Beliebte Beispiele

y^{''}+3y^'+2y=1,2e^ty(0)=2,y^'(0)=3

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, 2 e^{t} y (0) = 2, y^{^{'}} (0) = 3

y^{''}+y^'=e^x+x^3

y^{^{''}} + y^{^{'}} = e^{x} + x^{3}

y^{''}+ky=8sin(t)

y^{^{''}} + k y = 8 sin (t)

y^{''}+2y^'-3y=5e^{2x},y(0)=1,y^'(0)=a

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 1, y^{^{'}} (0) = a

(D^2+3D+2)y= 1/(4+e^x)

(D^{2} + 3 D + 2) y = \frac{1}{4 + e ^{x}}