y^{'''}-7y^{''}+10y=0,y^'(0)=1

Lösung

y^{^{'''}} - 7 y^{^{''}} + 10 y = 0, y^{^{'}} (0) = 1

y = - \frac{e ^{- 1.11039 \dots t} ( 1 - 1.32777 \dots c _{2} - 6.78262 \dots c _{3} )}{1.11039 \dots} + c_{2} e^{1.32777 \dots t} + c_{3} e^{6.78262 \dots t}

Schritte zur Lösung

y^{'''} (t) - 7 y^{''} (t) + 10 y = 0

Solve linear ODE:

y = - \frac{e ^{- 1.11039 \dots t} ( 1 - 1.32777 \dots c _{2} - 6.78262 \dots c _{3} )}{1.11039 \dots} + c_{2} e^{1.32777 \dots t} + c_{3} e^{6.78262 \dots t}

y = - \frac{e ^{- 1.11039 \dots t} ( 1 - 1.32777 \dots c _{2} - 6.78262 \dots c _{3} )}{1.11039 \dots} + c_{2} e^{1.32777 \dots t} + c_{3} e^{6.78262 \dots t}

7 x^{^{''}} + 3 x^{^{'}} + 7 x = 0, x (0) = - 4, x^{^{'}} (0) = 0

y^{^{'''}} - 21 y^{^{''}} + 128 y^{^{'}} - 240 y = 0

y^{^{''}} - 6 y^{^{'}} + 45 y = 0, y (0) = 4, y^{^{'}} (0) = - 6

24 y^{^{''}} + y^{^{'}} - 3 y = 0

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