y^{''}-9y^'=81x^2+7,y(0)=-1,y^'(0)=2

Lösung

y^{^{''}} - 9 y^{^{'}} = 81 x^{2} + 7, y (0) = - 1, y^{^{'}} (0) = 2

y = (- 1 + \frac{4}{3}) e^{9 x} - \frac{4}{3} - 3 x^{3} - x^{2} - x

Schritte zur Lösung

y^{''} (x) - 9 y^{'} (x) = 81 x^{2} + 7

Solve linear ODE:

y = (- 1 + \frac{4}{3}) e^{9 x} - \frac{4}{3} - 3 x^{3} - x^{2} - x

y = (- 1 + \frac{4}{3}) e^{9 x} - \frac{4}{3} - 3 x^{3} - x^{2} - x

y^{^{''}} - y^{^{'}} - 6 y = 14 sin (3)

y^{^{''}} + 2 y^{^{'}} + 5 y = 2 e^{(- t)} sin (2 t)

x^{^{''}} - 4 x^{^{'}} = 20 cos (5 t) - 4 sin (5 t) - 7

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

(\frac{d ^{2} y}{d x ^{2}} - 9 y) = e^{- 4 x} cos (e^{- x})