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

Lösung

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

y = c_{1} e^{\frac{( 7 + 13 ) x}{2}} + c_{2} e^{\frac{( 7 - 13 ) x}{2}} + \frac{x}{9} + \frac{7}{81}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{( 7 + 13 ) x}{2}} + c_{2} e^{\frac{( 7 - 13 ) x}{2}} + \frac{x}{9} + \frac{7}{81}

y = c_{1} e^{\frac{( 7 + 13 ) x}{2}} + c_{2} e^{\frac{( 7 - 13 ) x}{2}} + \frac{x}{9} + \frac{7}{81}

y^{^{''}} - 8 y + 20 y = 100 x^{2} - 26 x e^{x}

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

(D^{2} + D + 1) y = x e^{x}

y^{^{''}} + 2 y^{^{'}} - 8 y = 8 x^{2} - 3, y (0) = - 1, y^{^{'}} (0) = - 3

y^{^{''}} + y = sec^{3} (x), y (0) = 2, y^{^{'}} (0) = \frac{5}{2}