y^{''}-3y^'+2y=4x+3

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 x + 3

y = c_{1} e^{2 x} + c_{2} e^{x} + 2 x + \frac{9}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + 2 x + \frac{9}{2}

y = c_{1} e^{2 x} + c_{2} e^{x} + 2 x + \frac{9}{2}

y^{^{''}} + 6 y^{^{'}} + 5 y = - 9 e^{2 x}

y^{^{''}} + 18 y^{^{'}} + 81 y = x, y (0) = 0, y^{^{'}} (0) = 0

20 y^{^{''}} + 9 y^{^{'}} + x = 0, y (0) = 0, y^{^{'}} (0) = 3

so l v e f or d, d (x) = \frac{2 x ^{3} + 1}{x ^{6}}

y^{^{''}} + 9 y = 18 cos (3 x)