y^{''}+y^'=8x^2

Lösung

y^{^{''}} + y^{^{'}} = 8 x^{2}

y = c_{1} + c_{2} e^{- x} + \frac{8 x ^{3}}{3} - 8 x^{2} + 16 x

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} + \frac{8 x ^{3}}{3} - 8 x^{2} + 16 x

y = c_{1} + c_{2} e^{- x} + \frac{8 x ^{3}}{3} - 8 x^{2} + 16 x

y^{^{''}} + y^{^{'}} - 6 y = e^{4 x}

y^{^{''}} - 3 y^{^{'}} = 4 x

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

y^{^{''}} + y = e^{x} (6 - x)

x^{^{''}} + 6 x^{^{'}} + 9 x = 10 cos (2 t)