y^{''}+9y=2cos(3x)-3sin(3x)

Lösung

y^{^{''}} + 9 y = 2 cos (3 x) - 3 sin (3 x)

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

Schritte zur Lösung

y^{''} (x) + 9 y = 2 cos (3 x) - 3 sin (3 x)

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 3 = 0

y^{^{''}} + 3 y = 6 x

y^{^{''}} - 3 y^{^{'}} + 2 = 0

- 2 y^{^{''}} + 7 y^{^{'}} - y - 8 = - 6 x^{2} - 2 x^{3} e^{x}

y^{^{''}} - y^{^{'}} - 2 y = 4 t^{2}