1.
y' = e^(2x-y)
ln(y') = 2x-y
两边对x求导
y''/y' = 2 - y'
令y' = p
则y'' = dp/dx = dp/dy * dy/dx = pdp/dy
代入得
dp/dy = 2 - p
解得p = 2 - Ce^(-y)
即y' = 2 - Ce^(-y)
因为y' = e^(2x-y)
所以通解是
e^(2x-y) = 2 - Ce^(-y)
整理得
2e^y - e^2x - C = 0
2.
特征方程是2λ2+3λ-2=0
特征根λ = -2,1/2
通解是y = C1 e^(-2x) + C2 e^(x/2)