Toronto Math Forum
MAT244--2019F => MAT244--Test & Quizzes => Quiz-3 => Topic started by: lixinze2 on October 11, 2019, 02:00:26 PM
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Question: Find a differential equation whose general solution is $y = c_1e^{2t}+c_2e^{-3t}$
Since the solution is the linear combination of $y_1=e^{2t}$ and $y_2=e^{-3t}$
So,consider $r_1=2$ and $r_2=-3$ such that $(r-2)(r+3)=0$
So, $r^2+r-6=0$
Therefore, we know the equation $y''+y'-6y=0$ satisfies our solution