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

Lösung

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

y = e^{\frac{x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{1}{4} + \frac{x + sin ( x ) + cos ( x )}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{1}{4} + \frac{x + sin ( x ) + cos ( x )}{2}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{1}{4} + \frac{x + sin ( x ) + cos ( x )}{2}

y^{^{'''}} - y = e^{- x} + x (e^{x} + 1)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = x e^{x}

x^{^{''}} + 200 x^{^{'}} + 100000 x = 100 sin (100 t)

2 y^{^{''}} + 6 y^{^{'}} + 10 y = 4 cos (t)

y^{^{''}} - 14 y^{^{'}} + 49 y = 2 x e^{7 x}