y^{''}-8y^'+16y=24x+2,y(0)=2,y^'(0)=-1

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = 24 x + 2, y (0) = 2, y^{^{'}} (0) = - 1

y = \frac{9}{8} e^{4 x} - 7 e^{4 x} x + \frac{3 x}{2} + \frac{7}{8}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = 24 x + 2

Solve linear ODE:

y = \frac{9}{8} e^{4 x} - 7 e^{4 x} x + \frac{3 x}{2} + \frac{7}{8}

y = \frac{9}{8} e^{4 x} - 7 e^{4 x} x + \frac{3 x}{2} + \frac{7}{8}

y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + 3 y = e^{- t} + sin (t)

\frac{d ^{2} y}{d x ^{2}} + 100 y = 1000 sin (10 x)

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 3 + x^{- 1} e^{x}

y^{^{''}} - y^{^{'}} + 324 y = 18 sin (18 t)

y^{^{'''}} - y^{^{'}} = 9 sin (t)