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

Lösung

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{3}{4} e^{2 x} x^{2} sin (2 x) - \frac{3}{2} e^{2 x} x cos (2 x) + \frac{9}{8} e^{2 x} sin (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{3}{4} e^{2 x} x^{2} sin (2 x) - \frac{3}{2} e^{2 x} x cos (2 x) + \frac{9}{8} e^{2 x} sin (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} - \frac{3}{4} e^{2 x} x^{2} sin (2 x) - \frac{3}{2} e^{2 x} x cos (2 x) + \frac{9}{8} e^{2 x} sin (2 x)

y^{^{''}} + y = - 8 e^{3 t}

y^{^{''}} - 3 y^{^{'}} - 4 y = - 8 e^{t} (cos (2 t))

y^{^{''}} + y^{^{'}} - 12 y = - 32 t + 24 t^{2}

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

y^{^{''}} + 9 y^{^{'}} + 14 y = 3 sin (2 x)