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

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{2 x} x}{5} + \frac{- x ^{2} + 3 x}{2} - \frac{13}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{2 x} x}{5} + \frac{- x ^{2} + 3 x}{2} - \frac{13}{4}

y = c_{1} e^{2 x} + c_{2} e^{- \frac{x}{2}} + \frac{e ^{2 x} x}{5} + \frac{- x ^{2} + 3 x}{2} - \frac{13}{4}

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{3 x} (2 + 8 x - 12 x^{2})

y^{^{''}} + 20 y^{^{'}} + 125 y = 9 sin (5 x)

y^{^{''}} + y^{^{'}} - 2 y = e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{1}{x}

x^{^{''}} + 4 x^{^{'}} + 4 x = 100 sin (4 t)