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Beliebt Rechnen >

y^{''}+25y=20sin(5x)+xcos(x)

Lösung

y^{^{''}} + 25 y = 20 sin (5 x) + x cos (x)

Lösung

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 2 x cos (5 x) + \frac{x cos ( x )}{24} + \frac{1}{288} sin (x)

Schritte zur Lösung

y^{''} (x) + 25 y = 20 sin (5 x) + x cos (x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 2 x cos (5 x) + \frac{x cos ( x )}{24} + \frac{1}{288} sin (x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 2 x cos (5 x) + \frac{x cos ( x )}{24} + \frac{1}{288} sin (x)

Graph

Beliebte Beispiele

2y^{''}-13y^'+20y=40x^2+8x+10

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 40 x^{2} + 8 x + 10

-ay^{''}+by-1=0

- a y^{^{''}} + b y - 1 = 0

y^{'''}-24y^{''}+192y^'-512y=e^{8x}

y^{^{'''}} - 24 y^{^{''}} + 192 y^{^{'}} - 512 y = e^{8 x}

y^{'''}+18y^{''}-864y=e^{-12x}

y^{^{'''}} + 18 y^{^{''}} - 864 y = e^{- 12 x}

y^{''}+4y=2sin(2t)+t

y^{^{''}} + 4 y = 2 sin (2 t) + t