Question

Найти общие решения уравнений

Answer 1

$y''-4y'+3y=10e^{3x}\lambda^2-4lambda+3=0\lambda_1=1;lambda_2=3\Y=C_1e^{x}+C_2e^{3x}\hat{y}=Axe^{3x}\hat{y}'=Ae^{3x}+3Axe^{3x}\hat{y}''=6Ae^{3x}+9Axe^{3x}\\6Ae^{3x}+9Axe^{3x}-4Ae^{3x}-12Axe^{3x}+3Axe^{3x}=10e^{3x}\2A=10\A=5\hat{y}=5xe^{3x}\y=Y+hat{y}=C_1e^{x}+C_2e^{3x}+5xe^{3x}$