A=\frac{1}{6}\\x^0|-5A+6B=0=>B=\frac{5}{36}\\y=Y+\hat{y}=C_1e^{2x}+C_2e^{3x}+\frac{x}{6}+\frac{5}{36}" alt="y''-5y'+6y=x\\k^2-5k+6=0\\k_1=2\ ;k_2=3\\Y=C_1e^{2x}+C_2e^{3x}\\\hat{y}=Ax+B=\frac{x}{6}+\frac{5}{36}\\\hat{y}'=A;\hat{y}''=0\\-5A+6Ax+6B=x\\x|6A=1=>A=\frac{1}{6}\\x^0|-5A+6B=0=>B=\frac{5}{36}\\y=Y+\hat{y}=C_1e^{2x}+C_2e^{3x}+\frac{x}{6}+\frac{5}{36}" align="absmiddle" class="latex-formula">