y^{''}+2y^'+5y=30x^3+2

Lösung

y^{^{''}} + 2 y^{^{'}} + 5 y = 30 x^{3} + 2

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 6 x^{3} - \frac{36 x ^{2}}{5} - \frac{36 x}{25} + \frac{482}{125}

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 5 y = 30 x^{3} + 2

Solve linear ODE:

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 6 x^{3} - \frac{36 x ^{2}}{5} - \frac{36 x}{25} + \frac{482}{125}

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 6 x^{3} - \frac{36 x ^{2}}{5} - \frac{36 x}{25} + \frac{482}{125}

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 12 e^{t}, y (0) = - 1, y^{^{'}} (0) = 7

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

y^{^{''}} + y^{^{'}} - 2 y = 2 x + 3, y (0) = 1, y^{^{'}} (0) = - 4

y^{^{''}} + 5 y^{^{'}} + 4 y = 10 t e^{5 t}