y^{''}+25y=14cos(5x)+21sin(5x)

Lösung

y^{^{''}} + 25 y = 14 cos (5 x) + 21 sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7 x sin ( 5 x )}{5} - \frac{21 x cos ( 5 x )}{10}

Schritte zur Lösung

y^{''} (x) + 25 y = 14 cos (5 x) + 21 sin (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7 x sin ( 5 x )}{5} - \frac{21 x cos ( 5 x )}{10}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{7 x sin ( 5 x )}{5} - \frac{21 x cos ( 5 x )}{10}

l in e a r y^{^{''}} - y = t, y (0) = 0, y^{^{'}} (0) = 1

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

y^{^{''}} - y^{^{'}} = 5 e^{2 x}

y^{^{''}} - y - 2 y = 1 + t

y^{^{''}} + 5 y = g (t), y (0) = - 1, y^{^{'}} (0) = 0