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

解答

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

y = (7 - c_{2} - c_{3}) e^{- 1.11039 \dots t} + c_{2} e^{1.32777 \dots t} + c_{3} e^{6.78262 \dots t}

求解步骤

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

求解线性方程:

y = (7 - c_{2} - c_{3}) e^{- 1.11039 \dots t} + c_{2} e^{1.32777 \dots t} + c_{3} e^{6.78262 \dots t}

y = (7 - c_{2} - c_{3}) e^{- 1.11039 \dots t} + c_{2} e^{1.32777 \dots t} + c_{3} e^{6.78262 \dots t}