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Beliebt Rechnen >

(D^2+D+1)y=e^xsin(x)

Lösung

(D^{2} + D + 1) y = e^{x} sin (x)

Lösung

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + \frac{2}{13} e^{x} sin (x) - \frac{3}{13} e^{x} cos (x)

Schritte zur Lösung

(D^{2} + D + 1) y = e^{x} sin (x)

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + \frac{2}{13} e^{x} sin (x) - \frac{3}{13} e^{x} cos (x)

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + \frac{2}{13} e^{x} sin (x) - \frac{3}{13} e^{x} cos (x)

Graph

Beliebte Beispiele

y^{''}+9y=5sin(3x),y(0)=2,y^'(0)=0

y^{^{''}} + 9 y = 5 sin (3 x), y (0) = 2, y^{^{'}} (0) = 0

y^{''}+25y= 1/100 cos(5x)

y^{^{''}} + 25 y = \frac{1}{100} cos (5 x)

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

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

(d^2x)/(dt^2)-6(dx)/(dt)-7x=6

\frac{d ^{2} x}{d t ^{2}} - 6 \frac{d x}{d t} - 7 x = 6

1/6 y^{''}+6y=2tan(6t)-1/3 e^t

\frac{1}{6} y^{^{''}} + 6 y = 2 tan (6 t) - \frac{1}{3} e^{t}