y^{''}+2y^'-2y=5sin(x)-10xe^x

Lösung

y^{^{''}} + 2 y^{^{'}} - 2 y = 5 sin (x) - 10 x e^{x}

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} - \frac{15}{13} sin (x) - \frac{10}{13} cos (x) - 10 x e^{x} + 40 e^{x}

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) - 2 y = 5 sin (x) - 10 x e^{x}

Solve linear ODE:

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} - \frac{15}{13} sin (x) - \frac{10}{13} cos (x) - 10 x e^{x} + 40 e^{x}

y = c_{1} e^{(- 1 + 3) x} + c_{2} e^{(- 1 - 3) x} - \frac{15}{13} sin (x) - \frac{10}{13} cos (x) - 10 x e^{x} + 40 e^{x}

y^{^{''}} - 8 y^{^{'}} + 17 y = - 102, y (0) = - 3, y^{^{'}} (0) = 8

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

y^{^{'''}} + 2 y^{^{''}} + 4 y^{^{'}} + 8 = 0

y^{^{''''}} - 16 y^{^{''}} = x^{2} + e^{2 x}

y^{^{''}} - 4 y = sin (3 t)