2y^{''}-6y^'+3y=4sin(3x)+6x

Lösung

2 y^{^{''}} - 6 y^{^{'}} + 3 y = 4 sin (3 x) + 6 x

y = c_{1} e^{\frac{( 3 + 3 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 ) x}{2}} - \frac{20}{183} sin (3 x) + \frac{8}{61} cos (3 x) + 2 x + 4

Schritte zur Lösung

2 y^{''} (x) - 6 y^{'} (x) + 3 y = 4 sin (3 x) + 6 x

Solve linear ODE:

y = c_{1} e^{\frac{( 3 + 3 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 ) x}{2}} - \frac{20}{183} sin (3 x) + \frac{8}{61} cos (3 x) + 2 x + 4

y = c_{1} e^{\frac{( 3 + 3 ) x}{2}} + c_{2} e^{\frac{( 3 - 3 ) x}{2}} - \frac{20}{183} sin (3 x) + \frac{8}{61} cos (3 x) + 2 x + 4

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 7 + 7

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

y^{^{''}} + 16 y = cos (4 t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{(- 3)} e^{3} x