y^{''}+25y=8cos(5x)+12sin(5x)

Lösung

y^{^{''}} + 25 y = 8 cos (5 x) + 12 sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{4 x sin ( 5 x )}{5} - \frac{6 x cos ( 5 x )}{5}

Schritte zur Lösung

y^{''} (x) + 25 y = 8 cos (5 x) + 12 sin (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{4 x sin ( 5 x )}{5} - \frac{6 x cos ( 5 x )}{5}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{4 x sin ( 5 x )}{5} - \frac{6 x cos ( 5 x )}{5}

y^{^{''}} - 6 y^{^{'}} + 25 y = 2 sin (\frac{x}{2}) - cos (\frac{x}{2})

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 2 x} sin (x)

y^{^{''}} + 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{2 x}

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