(d^2-2d+5)y=e^{2x}*sin(x)

Lösung

(d^{2} - 2 d + 5) y = e^{2 x} \cdot sin (x)

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

y^{^{''}} + 9 y = 2 x^{2} e^{3 x} + 5

y^{^{''}} - y^{^{'}} - 12 y = - 5 e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

x^{^{''}} + 16 x^{^{'}} = 144, x (0) = 5, x^{^{'}} (0) = 12

y^{^{''}} - 90 y = sin (2 x)