y^'+y^{''}=y^{'''}

Lösung

y^{^{'}} + y^{^{''}} = y^{^{'''}}

y = c_{1} + c_{2} e^{\frac{( 1 + 5 ) t}{2}} + c_{3} e^{\frac{( 1 - 5 ) t}{2}}

Schritte zur Lösung

y^{'} (t) + y^{''} (t) = y^{'''} (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{\frac{( 1 + 5 ) t}{2}} + c_{3} e^{\frac{( 1 - 5 ) t}{2}}

y = c_{1} + c_{2} e^{\frac{( 1 + 5 ) t}{2}} + c_{3} e^{\frac{( 1 - 5 ) t}{2}}

y^{^{''}} + 9 y^{^{'}} - 9 y = 0

8 y - 2 y^{^{'}} + 6 y^{^{''}} - y^{^{''}} = 0

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

y^{^{''}} - 11 y + 18 y = 0

2 x^{^{''}} + 11 x^{^{'}} + 5 x = 0