y^{''}-6y^'+10y=10x^2+8x

Lösung

y^{^{''}} - 6 y^{^{'}} + 10 y = 10 x^{2} + 8 x

y = e^{3 x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2} + 2 x + 1

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 10 y = 10 x^{2} + 8 x

Solve linear ODE:

y = e^{3 x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2} + 2 x + 1

y = e^{3 x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2} + 2 x + 1

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

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

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

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

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