Question

ПОМОГИТЕ ПЖ МНЕфывфыв

Answer 1

Ответ:

$y''-3y'+2y=0\ \ ,\ \ \ y(0)=0\ ,\ y'(0)=2\\\\k^2-3k+2=0\ \ ,\ \ k_1=1\ ,\ k_2=2\\\\y_{obshee}=C_1\, e^{x}+C_2\, e^{2x}\\\\\\y(0)=C_1+C_2=0\\\\y'(x)=C_1\, e^{x}+2C_2\, e^{2x}\\\\y'(0)=C_1+2C_2=2\\\\\left\{\begin{array}{l}C_1+C_2=0\\C_1+2C_2=2\end{array}\right\ \ominus \ \left\{\begin{array}{ccc}C_1=-C_2\\-C_2=-2\end{array}\right\ \ \left\{\begin{array}{l}C_1=-2\\C_2=2\end{array}\right\\\\\\y_{chastnoe}=-2\, e^{x}+2\, e^{2x}$