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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 3 y = 9 x^{2}

y^{^{''}} + 6 y^{^{'}} - 7 y = 21 x^{2} - 8 x - 30

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x + 4, y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 9 y = 5 x, y (0) = 1, y^{^{'}} (0) = 3