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

Lösung

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

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} + 12 x + 13

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} + 12 x + 13

y = c_{1} e^{x} + c_{2} x e^{x} + 3 x^{2} + 12 x + 13

y^{^{''}} - 7 y^{^{'}} = t^{2}

y^{^{''}} - y^{^{'}} + 2 = 0

y^{^{''}} - 5 y^{^{'}} + 6 y = - 4 e^{3 x} + 10 e^{x} - 12

y^{^{''}} - y^{^{'}} = - 3 x + e^{x}

y^{^{''}} + y = cos (- t + \frac{π}{2})