y''-y'=x齐次通解Y:r²-r=0r(r-1)=0r1=0,r2=1Y=c1+c2e^x非齐次特解y*设特解形式为y*=x(ax+b)=ax²+bxy*'=2ax+by*''=2a2a-2ax-b=x-2a=1, 2a-b=0a=-1/2, b=-1y*=-1/2x-1所以通解为y=Y+y*=c1+c2e^x-1/2x-1
