Toronto Math Forum
MAT2442018F => MAT244Tests => Quiz3 => Topic started by: Victor Ivrii on October 12, 2018, 06:04:24 PM

Find a differential equation whose general solution is
$$y=c_1e^{t/2}+c_2e^{2t}.$$

in the attchement

$$
y=c_1e^{\frac{1}2t} + c_2e^{(2t)}
$$
$$
r_1=\frac{1}2, r_2=2
$$
$$
(r+\frac{1}{2})(r+2) = 0
$$
$$
r^2+ 2r+\frac{1}2r +1 = 0
$$
Therefore
$$
r^2+\frac{5}{2}r+1 = 0
$$
$$
2r^2 + 5r +2 = 0
$$
$$
2y''(t) + 5y'(t) + 2y(t) = 0
$$

$$
r=\frac{1}{2}or2
$$
$$
(r+\frac{1}{2})(r+2) = 0
$$
$$
r^2+ 2r+\frac{1}2r +1 = 0
$$
$$
r^2+\frac{5}{2}r+1 = 0
$$
$$
2r^2 + 5r +2 = 0
$$
Therefore
$$
2y'' + 5y' + 2y = 0
$$

Yuki, only ASCII file names!