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Beliebt Rechnen >

y^{''}-4y^'+13y=sin(3x)

Lösung

y^{^{''}} - 4 y^{^{'}} + 13 y = sin (3 x)

Lösung

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{1}{40} sin (3 x) + \frac{3}{40} cos (3 x)

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 13 y = sin (3 x)

Solve linear ODE:

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{1}{40} sin (3 x) + \frac{3}{40} cos (3 x)

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{1}{40} sin (3 x) + \frac{3}{40} cos (3 x)

Graph

Beliebte Beispiele

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

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

y^{''}+y^'-12y=-sin(2x)+3cos(2x)

y^{^{''}} + y^{^{'}} - 12 y = - sin (2 x) + 3 cos (2 x)

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

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

x^{''}+25x=2cos(5t)

x^{^{''}} + 25 x = 2 cos (5 t)

x^{''}+9x=sin(3t)

x^{^{''}} + 9 x = sin (3 t)